In Catcher in the Rye, why does Holden think it spoils a conversation if someone asks what religion he is?

Holden is obsessed with the idea of authenticity, and he seems to feel that when people find out what religion a person belongs to, it makes them look at that person in a certain way.  After that, they are no longer able to see and appreciate the person for whom they really are.  In his own experience, Holden says that people are always trying to find out if he is Catholic, because his "last name is Irish, and most people of Irish descent are Catholics".  He cites the example of a time when he met a Catholic boy, Louis Shaney, at the Wooton School, with whom he

"struck up this conversation about tennis.  (Louis) was quite interested in tennis, and so was I.  He told me he went to the Nationals at Forest Hills every summer, and I told him I did too, and then we talked about certain hot-shot tennis players for quite a while.  He knew quite a lot about tennis, for a kid his age.  He really did.  Than, after a while, right in the middle of the goddam conversation, he asked me, 'Did you happen to notice where the Catholic church is in town, by any chance?'  The thing was, you could tell by the way he asked me that he was trying to find out if I was a Catholic...He was enjoying the conversation about tennis and all, but you could tell he would've enjoyed it more if I was a Catholic and all..."

Holden feels that once people have classified you as being of a certain religion, it changes the way they relate to you; their ability to see you as you really are is clouded by the attributes they begin to ascribe to you because of the group with which you are affiliated.  Holden actually says that "that kind of stuff" doesn't exactly "spoil" a conversation, but it makes it different.  He says that it "(doesn't ruin a) conversation or anything...but it sure as hell (doesn't) do it any good" (Chapter 15).