One of the problems with taking D&D literally is where to begin.
Most people start D&D with the PHB. So let's try that. (Please note that I am still using the 3.0 PHB, so YMMV)
The first thing we learn is that everyone is measureable in six attributes. This suggests something like IQ tests with six specific categories. People know about their own results and might share them with others, but not necessarily so. We also find that people who have a high Wisdom score are both terribly observant and very much in touch with their gods, which might be an aspect of semi-omniscience. Charisma is a hard statistic to quantify, however -- there are implications that this statistic represents belief in yourself (but Wil saves are made off WIS), a sparkling personality, and the ability to speak well -- one wonders which aspect fuels sorcerous magic. Still, we can put that aside as strictly being mechanics, so let's move on.
The next thing we learn about is a character's race. Now there are several interesting notions spring up from this chapter. First of all, we find that Humans can interbreed with Elves and Orcs, but not with other races, nor are Orcs and Elves apparently able to interbreed with each other. This is rather quizzical. We also learn very quickly that seven different "races" (more correctly "species") live together in multiple communities with very little serious racial tension. Equally, we find out that there is a single language (Common) that almost everyone learns, especially the "core races", thus removing all barriers to basic communications, yet most races retain their own languages as well; why do they do this? Also everyone is literate, a major accomplishment (of course this will be contradicted under Classes, but let's keep that under our hat for the moment). We learn that dwarves are little loved and/or have very dull speech patterns and/or just fail to make a major impression on people (-2 CHA), elves are unhealthy (-2 CON) yet live very long lives (one wonders how), etc. Another question that leaps to mind, however, as all these races live, work, and play together, is what style of housing would come to predominate? You have two exceptionally short races -- this means that the taller races would probably not be able to enter their homes and that the shorter races would have difficulty in most shops run by taller folks. Might this lead to ghettos of Shorts amongst the Talls?
The next point is one's Class is important. There are 11 Classes that people fit into, each attracting different sorts of individuals, sorted by their attributes and desires. (We later find out that there are also NPC classes, but that's not until the DMG.) We find that very strong people would want to be Fighters, very tough people would want to be Barbarians (the only class that is not literate), very quick people gravitate towards being Rogues (all of whom are assassins as they all gain Sneak Attack), very smart people are drawn to being Wizards, very insightful people (and very observant people) feel comfortable as Clerics and very personable individuals (or very egotistical people, or very good talkers) become Sorcerers.
A few wise folks become enamoured with the Druid class, but those who are strong, tough, and wise tend to become Monks. Consider this immediately -- we know that not only is the world of "reality D&D" polytheistic, as shown by the Clerics, but also polyreligious. Druids do not worship the same gods (except in a few cases) that the Clerics do and even when there is a crossover they worship in a different manner.
But let us look at each class and see how it would affect society.
Barbarians would probably not be trusted within cities simply for their tendency to go whacko and start hitting things. Yes, this is a controllable talent and has a limited number of uses, so perhaps there are patrols in town who go around provoking Barbarians until they rage a given number of times per day and then let them go about their business. Barbarians, however, are also notoriously jumpy (Uncanny Dodge) and would probably come off as paranoid. Overall, society would be happiest to keep them far away from other people. And their literacy problem would probably make them objects of derision and scorn in the otherwise literatre world. Top this off with the fact that Barbarians cannot be Lawful (Alignment working as an Absolute), structured societies would again have little reason to trust them.
Bards would be welcome many places simply due to their reliance on CHA. On the other hand, their music is of an odd effect. How often is Inspire Courage necessary in a community? Fascinate would lead to questions about business contracts and crimes -- there would undoubtably have to be laws curtailing its use. Conversely Inspire Competence would be loved by all business owners -- I can imagine Bard Muzak being popular for important projects. Suggestion becomes even more notorious -- see Fascinate above, but more so. Inpsire Greatness could be used under very specific circumstances, but on a day-to-day level it would be considered quite dangerous ("What?!? You went to a bar, a brawl broke out, and you started singing?!? Lock him up!"). Bards would also be noted as private eyes, stoolies, spies, and informers, due to their Bardic Knowledge -- useful to specific people at specific times, but the trust might be lacking by their opposite numbers. Again, Bards cannot be Lawful (Alignment as an Absolute), so structured and orderly societies (Lawful) might not fully trust them.
Clerics prove that gods exist. Sort of. On the one hand, they have spells directly from their gods; on the other hand, almost everything they can do, wizards and sorcerers can do. Most people would accept Clerics at face value as absolute proof of the existence of gods, while a few malcontents would seem them strictly as hyperspecialized wizards. On the other hand, Clerics do not have to actually worship a god, they can worship a Principle (Law, Chaos, Good, Evil, either form of Neutral, as well as specific Domains, which some people would say are aspects of gods while others would say are Schools of Magic). They control the undead, either by driving them off or by giving them orders, which suggests, since this is a low-level and easily obtainable power, that a lot of people in the world refuse to stay dead. Reg Shoe, eat your heart out. Clerics are well known as healers and this might or might not lead to healthier communities, depending on how many clerics there are, how willing they are to grant their healing touch, etc. It is also interesting to note that there is a suggestion of strong and open inter-faith conflict in that all Clerics are fairly well versed in the use of arms and armour, not to mention have good hit points. Do religious conflicts happen that often in this world and are they militant rather than intellectual? Good, Evil, Law and Chaos become obvious defined traits here as well, in that many spells are not open to Clerics of differing backgrounds. Alignment, therefore, works as an Absolute.
Druids are like Clerics, but they work more with the natural world. As to Alignment, they "must maintain at least some measure of dispassion" and "must be neutral in some way, if not true neutral". This makes them very cliquish. Druids have a very limited range of weapons they may use as well as an injunction against metal armour (but not metal weapons -- we see the scimitar on the list, as well as other items that are often, though not invariably, made of metal). Yet is not metal derived from nature? An odd injunction that might spur much debate in their communities. That being said, Druids will probably not be found often in cities as they obviously get along well in the wilds -- this suggests that Barbarians, Druids, and Rangers form communities away from city walls. Might segregation then take place due to philosophy and class rather than by ethnicity and religion? In any case, Druids are always followed by at least one wild animal, again not making them overly welcome in cities.
Fighters are fighters are fighters. They are well-trained at a set of skills that are terribly useful, but under very limited circumstances in a Real World society. Still, as we find out in the DMG, there are a lot of Fighters; this suggests that the Monster Manual should be taken very seriously and that the world is far more dangerous than our own. Perhaps this should be balanced with the vision of all those undead that the Clerics need to turn (or control) on such a regular basis.
Monks are odd ducks. They must be Lawful (Alignment as Absolute) and they may not switch to another Class and back again. Once a Monk, always a Monk, or never a Monk again. One wonders if this is because the other Monks refuse to take a slacker back (organization rules of a highly Lawful, thus Orderly, group) or if there is some sort of gene that kicks in that doesn't allow the person to start up again once they have dropped off the path. In any case, many Monks would likely be employed as patrolmen in cities -- they never really need their weapons, they can get to the scene of a crime quickly, and they are inherently Lawful. This sounds like a great combination. Also having high Saving Throws across the board means they are better able to resist almost anything thrown at them.
Paladins are the most restricted, must curtailed class going. They must be Lawful Good (though they do not need to worship a god, even though all their power seems to be religious). Any deviance from the path makes them lose their powers. Unlike Monks, however, Paladins are allowed to multiclass, which suggests that the rules governing groups of Paladins are more open and forgiving. Paladins are going to appeal to a very limited group of individuals, not only due to the Alignment restriction, but also due to the fact that they need decent scores in nearly every Attribute. This suggests that Paladins, rather than being the Best and the Brightest, are more often the Most Consistently Slighty Above Average. Sounds like an odd group for the gods of Law and Good to funnel their powers through, but there it is. Leaders of Society would love these guys as military officers due to their Aura of Courage and not having to provide them with a horse, yet would have problems with them in this role as they would have to justify every single action to them. In the end many people would admire Paladins, while not wishing to copy them.
Rangers, like Druids and Barbarians, would not often be seen in cities. Why bother then all of their skills are focused on being outdoors. Many people would also look upon Rangers as rather psychotic -- why do they have such deep-seated hatred against broad categories of creatures? If the Favoured Enemy were Animals, this might simply suggest being good hunters, but what of Abberations or Goblinoids? Many Rangers seem to have a chip on their shoulders the size of a Sequoia. Of course the other answer might be simpler -- through Fighters and Clerics we have already seen that this world is inherently and highly dangerous, so maybe having specialist snipers as a first line of defence is necessary. In any case, they can find their "prey" (enemy, an odd choice of terms) more easily than most and then dispatch them relatively quickly. The interesting thought is the continual training process for Rangers as they learn about more and more Favoured Enemies -- is there a school that teaches where to shoot a Beholder or stab an Ochre Jelly?
Rogues, as noted before, are probably not the most trustworthy folks in society. First of all, each one of them is an assassin -- they all gain Sneak Attack, and this only gets worse as they get higher. Like the Barbarian they tend to be jumpy and nerous (Evasion, Uncanny Dodge, etc.). We can also see that there must be a fair number of locks and cunning traps set up in this world as they Rogue is there to frustrate them (and, as we see from the DMG, there are a lot of Rogues in society). So security measures are fairly prevalent, but did that come about because of the Rogues, or vice versa? Hard to tell. In any case, unlike pretty much anyone else, Rogues can find and remove traps; this suggests also that Rogues also work in security (Set a thief to catch a thief). Another interesting aspect of Rogues is that they are so talented, having large numbers of skill points. Might a great number of them be craftsmen and various other types of professionals? Indeed, might not the best merchant in the world be a fully trained Rogue, thus making you suspect traveling salesmen even more? ("You sure you're not an encyclopedia salesman?" "No, ma'am, I'm just a burglar.")
Sorcerers are an odd lot. First of all, most people can't help but like and trust them, due to their high Charisma, but on the other hand have all that magic. They are usually identifiable due to having an animal tagging along after them and, unlike Druids, they do not necessarily look like they've been sleeping in the outdoors. This is especially notable since Sorcerers are so fragile. These are not creatures who go wandering around without bodyguards (thus suggesting the reason adventuring parties form in the first place is often because a Wizard or Sorcerer wants to go someplace dangerous and has the need of meatshields). Of course someone this popular will have no proble gaining guards. Sorcerers would be quickly summed up by the local constabulary depending on the type of magic they can cast. Are they Wandering Weapons Platforms? Watch 'em close or lock 'em up. Are they Support Spell Casters? Watch them somewhat less carefully. Are they the type that chooses inoffensive, though potentially amusing, spells? Fine, let 'em go.
Wizards are less well liked then Sorcerers, but are probably admired for their deep intellect, much like physicists are admired at a distance. Like the Sorcerers, Wizards are usually followed by an animal. Also like the Sorcerer, Wizards do not go wandering in the Great Outdoors without a bodyguard, thus suggesting the reason that adventuring parties might form.
So what do we see here? A society where racial tensions are less important than religious tensions, as well as a strong split between City and Country. We see a highly dangerous world with a good amount of undead. We see a society that will probably have a fair little constabulary to watch over the doings of the "classed characters". And we see cities where there are interesting divisions based on size.
More to come? Who knows...