In addition to some of the engaging theoretical discussion herein, I wanted to offer a practical suggestion, as well. I hope it proves not only useful, but also reinforces some of the sentiments, ideas, and notions that Brad (Bawylie), Imaculata, and others have been invoking in their own contributions.
Part of establishing any cultural component in a role-playing game is not just the underlying mechanics, but the descriptive story elements, as well. Obvious statement, but I bring it up (and I think it fits with Bawylie's previous comment) as a point in establishing credibility.
So, the basic rules in role playing games may give pantheons, and talk about things like domains, and alignments, and so forth, and some games even go further and describe things like favored weapons or clerical vestments or holy days.
But I'd like to suggest that part of building the world in which the religious aspects are credible enough to be taken seriously (for various values of "seriously") is front-loading the world with much more (and I think this follows on what Imaculata has mentioned about D&D pantheons/religions being shallow) than the standard content in most basic rules of rpgs.
And all of this would be better taking place in conversation with the players (a vital component) before classes are even considered.
If a person wants to play a cleric, it might help their approach if they have information beforehand, not just alignment, and portfolio, not even just favored weapon and vestments. Describe particular beliefs. Describe specific rituals for specific days and times of day that clergy get up to, and specific rituals that laity get up to. Describe multiple different interpretations of a single doctrinal point. Describe the religion's history, including the heretical movements that were suppressed, the heretical movements that survive underground, the heretical movements later deemed orthodox, the heretical movements that splintered and formed reformations, the major historical figures in the religion, local historical figures, doctrine not just about theology but about things like economy, social policy, race relations, magic, politics, and more. Describe the religions thoughts on things like agriculture, sex, and labor relations. Describe the ways in which people like the religion. Describe the ways in which people complain about it. Describe the hopes, fears, and indifferences people have to the religions. Describe how much money it has, how much corruption, and how it manages its resources. Describe those components that have affect actual game mechanics, and describe even more that have no mechanical outcome whatsoever. Describe, describe, describe.
None of which is a guarantee that a particular player won't just want the "free heals" and access to church resources and roflcopter the rest, but it might help establish the religion beyond the basics. The rules are only ever likely to impart the basics, and if the basics are seen as nothing more than [CaptainBarbossa] "what you'd call 'guidelines'" [/CaptainBarbossa] they may be harder to regard seriously. If what you have is significant lore that doesn't just infiltrate the understanding of the world, but actually represents a necessary component to grapple with in order to engage with the world, then its easier to take seriously.
But never a guarantee, of course, and as so many have posted, if their heart's not in your interpretation of consideration then there's little you can do other than negotiate in hopes of finding compromise, or at least acknowledgement.
The other drawback to the approach of going really deep in regard to religious content in-game, is the amount of time you would have to invest, at risk of nothing in response. Of course, that's potentially any GM's risk. Which brings us back to the conversations you have with players before the game. Sometimes I feel like the basics of the rpg are there for the quick-and-dirty start, get straight to the action! That's fine, and can be fun, but if what you're hoping to do is build long-term storytelling with engaged play, I think it helps to have conversations about the game and hopes before the dice start clattering across the table. Maybe the players just want the basic and get straight to the action. Maybe it's a mixed group, with amateur thespians like me that want to go some measure to inhabiting characters, and some who just want to hit things and watch the numbers diminish until it's time to loot.
But the religions in game need to feel like they have serious (not the same thing as severe) components if they are to be taken seriously, and I suspect the basic rules outline may not be enough to get the ball rolling, or may be a little harder, at least.
Wow! Who opened my typing spigot to "floodwater"?
Still learning,
Robert