Much of the confusion comes from the many meanings of the word “respect”.
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A respectful argument might be one where I state my opinion of your opinion without resorting to insults or mockery.
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If I respect your right to do something, I may disagree with it but I will not use the law, violence of the threat of violence to stop you from doing it. I might still try to convince you or mock it.
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If I respect a rule, I obey it. “Respecting religion A” would then mean abiding by its prescriptions.
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Another kind of respect is located in-between the 2nd and 3rd option; I don’t have to obey it but I can’t argue forcefully that it’s erroneous.
Perhaps Illuminati has in mind the 4th kind of respect?
I can’t think of many good arguments for allowing forceful argumentation against beliefs but not religious beliefs, at least in places that aren’t close to civil war or where it just isn’t appropriate (like the aformentioned funeral, where that’s just being a disruptive cunt).
The people who want any but the 2nd type of respect are the same who protested The Life of Brian. They just don’t want their beliefs challenged and use the powerful and vague word “respect” to get you to shut up.
Aside form the issue of respect, there are times when it isn’t wise to challenge religious views. Sometimes, it just isn’t worth it and is likely to make the situation worse. But that’s a purely consequentialist consideration and not linked to any notion of respect. It’s the same reason that in some situations, you shouldn’t talk about potlics; too likely to make the social meeting awkward.