No it's not a standard part of learning how to play.
Moldvay Basic - one of the best-selling and most-played versions of D&D - suggests that a new player should read the monster chapter of the book.
It's also common for people who are going to DM to read modules in advance to run them or even just to see if they some day want to run them. The same logic you are applying to the MM still applies to modules.
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I've run the Desert of Desolation series at least 3 times. Well after that, a DM I used to play with decided to run it. I remembered many of the secrets. According to what you are saying here, it would have been okay for me to bring in my Uncle Cheap Justification to let me know all of those secrets via talks he had with me in my youth.
Not at all. In fact I posted the exact opposite of that:
it is very common for person A to be both a GM (sometimes) and a player (sometimes) and hence to have read the MM in the former capacity and to have that knowledge become relevant in the latter capacity.
Whereas for person A to have GMed a module which s/he is now playing in is (at least in my experience) less common, even unusual.
To elaborate yet further: whereas some versions of D&D direct new players to read the monster section (eg Moldvay Basic) and others are silent on the matter (AD&D, 3E, 4e); and whereas it is a ubiquitious feature of D&D play that one encounters the same monsters in new campaigns, and hence knows the weaknesses despite never having had this particular PC deal with them before; most modules that I'm familiar with have a bit somewhere near the start which says
Don't read this if you're going to play it as opposed to GM it.
In other words, the assumptions in D&D around
knowledge of monsters and
knowledge of modules are completely different. I can't believe that this is even remotely controversial.
If the relatively unusual situation comes up that this instruction is being violated - eg you are playing Desert of Desolation as a player despite having read it - then the table will have to make some decision about how to handle that, given that it is going directly against the instructions, and the premise about play (ie that players don't know the module) which those instructions are an expression of.
(Note also that none of this changes my point that there are other systems (DW) in which this whole issue cannot even arise.)
TL;DR EDIT: It's taken for granted in D&D play that the contents of the Monster Manual will be reused by the same people across multiple campaigns, multiple PCs, etc. It's therefore practically inevitable that any given player will experience a situation in play where s/he knows more about a monster's weaknesses that is prima facie likely for his/her PC.
The game provides no rules for actually dealing with this, because when the game was invented it was taken for granted that players, being good wargamers, would do what you call "metagaming" without anyone looking for an ingame rationale.
[MENTION=6785785]hawkeyefan[/MENTION]'s suggestion of how to generate an ingame rationale seems as good as any.
In contrast, it has never been assumed that the same player would play the same module again, or play a module s/he has GMed. In fact the instructions for most modules direct the opposite: that if you're going to play it then you should make sure not to learn the contents in advance.
So if this comes up for a group, that group is going outside the assumed and stated parameters of play. However this is handled, it can't just be
assumed to be the same as the ubiquitous, and intended to be ubiquitous, monster case.