The issue, in my view, here is that the DM expects certain out of character behavior from the players (he said himself that the issue is they're cracking jokes out of character). The DM can feel free to punish my character for in-game behavior all he wants, but he has zero right to control my behavior as a player. If I think something is ridiculous and make a joke about it, I'm sorry if that hurts your feelings, but you need to just accept that not everyone is going to be as involved in certain topics as yourself.
If, from previous session's experience, you have discovered that your group finds religion to be a subject for mockery, why is it THEIR fault when you keep presenting them with religious material to mock? If your group thought sports were ridiculous and you kept presenting them with sports related content, are you REALLY going to be surprised about them mocking your sports themed content? If your group thought that court-room dramas were bad television, are you really going to be surprised when they mock your court-room drama inspired campaign?
As a DM, you HAVE to take into account the attitudes and views of your players, and trying to shoe-horn your own views and interests into the players behaviors is only going to result in difficulties. I think that anime is awesome, I'm one of three people in my groups who hold that view. When I run, I don't run anime inspired content (maybe story wise I might steal an idea for an encounter setup, or try to incorporate a particular aspect, but no Naruto or Escaflowne games) precisely because the majority of my players have zero interest in anime. If you try to impose your reverence (not a pun, I revere history and religion, but I'm an atheist and my interests in it are not at all spiritual) for a particular subject onto people who have zero interest in that topic, you're going to come across as the dick in that situation.
Also, it absolutely is bullying; he is using his position of power to impose on the PLAYERS certain views and behaviors, it is EXACTLY like being the big guy in school and having people harass and (attempt to) punish you because you don't play football, or the attractive girl who is harassed and punished because she spends more time studying than partying. Just because it's not hitting someone with their own hands or calling them names does not mean that it is not still unethical to use your authority to compel someone into adopting a view or behavior that you find to be preferable. If the DM were trying to compel players to role-play heterosexual characters and they were homosexuals it would absolutely be bullying; the players clearly do not take religion seriously and the DM trying to use his authority to compel certain OOC behaviors, and that is immoral and wrong. If you don't like the OOC chatter that is a response to the scenario that you have presented, then stop presenting those scenarios. No amount of "adult" discussion is going to make the players suddenly find religion to be an interesting and compelling topic.
Also, the "adult" discussion here seems to be "Oh, well I've spent a lot of time working on this and I find it interesting, and I'm the one running the game, so now you guys also need to find it compelling and interesting because if you don't then I'm going to punish you in-game." That hardly sounds adult, as it is a self-centered position (I put in all this effort, I made this game for you players, I'm the one in charge). I have no problems with NPCs responding to IN-GAME character actions, it is obvious that, historically, societies have been exceedingly religious, so NPCs responding to PCs who are disrespectful of their traditions absolutely makes sense, and feel free to determine how religion influences your world however you want, that's fine. The problem I, and apparently others, have is when you attempt to control PLAYER behavior. That is right-out unacceptable, and I find it disturbing how many people here think that it is perfectly acceptable to force a group of other people to behave certain ways because of their own personal preference. I don't like beer, and I think most people when drunk are annoying as hell, but I wouldn't ban alcohol because I'm not a fan, that's a dick move.
Did you, from the outset, explain that your world would have a significant focus on religion? I suspect that this is not the case, I suspect that had you made it clear that your expected player respect for your fictional religions then you would have heard the problems your players have with such a concept, especially if they think religion is something to be made fun of (I myself am an avid mocker of religion, I consider it a hobby). If I was wanting to run a game where we explored the topic of beastiality (just using an absurd example here) and I didn't tell my players this beforehand, and then kept introducing them to scenes of interspecies "relationships" and then got upset because they made fun of it, it would entirely be my fault (zero interest in running a game like that, again, absurd example) as the players were expecting a traditional dungeons and dragons experience, and I gave them the chicken lover episode of south park combined with the seriousness of an episode of nova.
As DMs, we should give the players what they want; a fun and interesting game. If they don't find religion to be fun and interesting, then you, as the DM, are the one at fault for continuing to shove religion down their throat, not the players for voicing their disinterest and lack of reverence for the topic out of character. Clearly they know that you hear what they're saying, and obviously they take pains to establish that this chatter is out of character, so they are giving it as much effort as they need to. If their characters started openly mocking religion in-character, despite being a character that grew up in such a religious world, then yeah, they are being disruptive, in character, to the game world, and the gods and other NPCs are free to react however they deem appropriate, just as they are free to react to blatant thieves, strong-arm bullies, outright murderers, etc. Otherwise, it is a symptom of a larger problem; your imposition of a narrative that the players do not find compelling or interesting, hence their mocking of it out of character.
The players, in this situation, are the ones acting in good-faith and are portraying their characters to the best of their abilities. The OP is trying to tell a story that the players simply aren't invested in, that's not their fault, that's the DM's. If you want the game to continue to be fun for everyone (sounds to me like the players are making their own out of character fun) then you need to adjust your story to be more in-line with what the players find interesting. Otherwise, enjoy hearing about their distaste for the content until you get sick of it and quit or they get sick of it and quit, or both.
On a side note:
The only parts of the crunch of clerics relating to divinity is the Divine Domain feature where it explicitly states that your domain is derived from your deity, Channel Divinity where it explicitly states that you are channeling divine power from your deity, and Divine Intervention where it explicitly states it relies on your deity. It is not only bad form, but bad ruling to strip a cleric of their spellcasting ability due to a deity's whim as there is NOTHING in the spellcasting feature that requires adherence to a religion of any kind.
Further, I see no problem with atheist clerics (when I play an atheist cleric, I acknowledge the existence of the gods, I just view them as extremely powerful entities who have attained a certain level of power, and that anyone can achieve such a power through the accumulation of power and knowledge, so I don't worship any god, but instead weave divine forces, and this has presented quite a few interesting role-play opportunities and very few problems (it helps that I play with atheists, agnostics, pagans, wiccans, jews, and moderate christians), outside of how I interact with certain NPCs, usually religious NPCs such as clergy and faithful populations), and I, personally, would even let them choose a domain, channel divinity, and yes, even make use of divine intervention with zero complications (you, as a student of the divine arts have chosen a domain to focus on as a wizard chooses a school of magic to make their focus, you channel the ambient divine energy of the multiverse, and can on occasion call upon the divine nature of reality to intervene in some unforeseen manner) mechanically, because it's fluff. I've also played religious characters who had no mechanical reason to be religious either.
What is wrong with a divine wizard that doesn't use wizard spells? How did other creatures ascend to godhood? Aren't there a litany of gods who stole their power from another god, or simply got to that level themselves? In real world religion and in the fictional pantheons there are a number of deities that started out mortal and were able to achieve that state through hard work and dedication. Not saying you have to run your game that way, that's up to you as a DM, I'm just saying I don't think it's absurd to allow it.
Additionally, I have never seen anyone play a religious druid, but I have seen many people play druids who revered nature as a force (again I refer to the religious views of the players I play with) similar to how typical clerics revere their deity. I've never interpreted the druid class as a holy order that follows a deity, but rather as a "holy" order that works to preserve the natural world. In my view, divine, arcane, and primal power sources are just that; sources. If you get your powers through rote memorization and the manipulation of arcane forces, fine, just as I'm fine with the manipulation of divine forces and primal forces. But, that's a personal interpretation I don't expect anyone else to have. Some people, clearly, expect clerics and paladins to be beacons of religious piety, I think that's a narrow view to have.
I think the fluff regarding a class should have zero effect on the character you want to play; I wouldn't force a paladin to have a diety any more than I would force a fighter to, since I view the paladin as a martial character that also can wield divine energy, and the ranger as a martial character that can wield primal energy, etc. etc. so on and so forth. In my view, the classes are a set of mechanics to describe how your character can interact with the world in which they reside, not strict limits on how a character must interact with the world, which I suspect may be a significant difference between my view and the views of people who aren't fans of multi-classing.
P.S. - When I say it's bullying, I don't mean that I think the OP is a horrible person who is a bully, I mean that the tactic of trying to impose out of character behavior is analogous to bullying the same way that peer-pressure is a kind of bullying, it's unintentional. For the record, I think your story is probably a good story, but I suspect that's because I find religion to be interesting (though I'd probably still mock a few things here and there out of character, maybe even in character depending on the character I'd make).
