Why does Holden think it spoils a conversation if someone asks what religion he is in The Catcher in the Rye?
You can find the information from chapter 15 in the book, but the answer isn't exactly in the text.
Holden Caufield and his author J. D. Salinger both had parents of different religious faiths, so they are sensitive to religious phoniness and stereotyping. Salinger had one parent who was Catholic and one who was Jewish, so there was some religious identity issues and confusion. The same it is with Holden: he says his father was a Catholic once, but now he is an atheist.
In Chapter 15, however, Holden loves the fact that the nuns (who outwardly show their Catholic faith by wearing the habit) do not ask him if he's Catholic. He says:
That's why I was glad those two nuns didn't ask me if I was a Catholic. It wouldn't have spoiled the conversation if they had, but it would've been different, probably. I'm not saying I blame Catholics. I don't. I'd be the same way, probably, if I was a Catholic. It's just like those suitcases I was telling you about, in a way. All I'm saying is that it's no good for a nice conversation. That's all I'm saying.
Instead, the nuns discuss Mercutio, who--like Holden--refused to pick sides between the warring families. Rather, Mercutio cursed both houses. The same it is for Holden: he curses groups (religious or otherwise) who cluster together and have a mass identity. Notice that Holden doesn't have to lie to the nuns; he engages them honestly because they're not phony. He even gives them money.
Holden is an individual who aggressively asserts his own religious free agency and refuses to commit to the mass phoniness of the watered-down religion, prep-school "good old boy" network, or the materialistic consumer culture of the 1950s. Instead, he enjoys conversations about literature with other book lovers who are not consumed with appearances, money, or status.