@semck:
"I don't know if religious beliefs are just "background," though. Sure, if somebody has left their faith, but I think that's a different statement than saying that you don't care about somebody's religious beliefs."
Well, since I'm an atheist...I don't view any religious belief as being one I think is true, so I don't care about them on that basis...
I have Catholic friends, Mormon friends, Jewish friends, Muslims, some different Protestant denominations in there, so I run the gamut. (And then of course I have atheist/agnostic friends, whom I list here separately since I don't like the view that somehow atheism = another religion...as atheism the non-belief in a deity/religion. And you know what I mean by that, let's not nitpick the dictionary definition.)
The point of all that being--yeah, when I hear my Catholic friends go on about their beliefs, or Mormon friends talk about theirs, or any group above talk about them...I think they're wrong and, if I'm honest, there are plenty of times where I personally find those beliefs silly (for example...I hear Mormon friends say what they believe about the Garden of Eden being located in America, or Jesus being in America, or Native Americans and Jews somehow being connected, and I sit there...these being some of the absolute nicest people I've ever met...and internally, I'm just, "WHAAAATTTTT?!?!?!" :p )
But that's me. There's plenty of stuff *I* do or say that's silly, and I'm sure they giggle internally at those things as well. (We can all think of examples of my saying something silly, I'm sure.) ;) In the same way someone can disagree with me on Shakespeare, I can disagree with them on things I don't agree with, and it's all good, just a background thing in our larger relationship.
Religious beliefs, when they're kept personal, are none of my business.
If someone makes their views public, and argues for something I disagree with on religious grounds--ie, against gay activism--then it becomes something more and not just a background element of our friendship.
To be unfair and pick on Mormonism again--because unlike my nice Mormon friends, I'm a prick--I said during the 2012 Presidential elections that, while normally I just accept the fact politicians need to be/claim Christian faith in order to get elected in the United States, and that normally that doesn't bother me, it *would* with Mitt Romney *BECAUSE* of what his religion specifically said about blacks being somehow "fallen" during the time in which he would've been growing up in that Church.
Given the fact that, you know, race is kinda-sorta a major deal in America now (has it never not been?) with recent events, that would impact whether or not I'd vote for a Mormon who sincerely believed that, NOT because of their religious belief in Jesus or an afterlife or any of that, but simply because viewing blacks as somehow being "fallen" might, you know, kinda-sorta-maybe color the way you view race relations and thereby alter policy decisions, and THAT is what I care about.
TL;DR:
If your religious views are personal and kept to yourself, unless they come up naturally in conversation, then it can be background with me, and be on the same level as what your ethnicity/ancestry is...being of Iranian ancestry with Persian relatives will color who you are, yeah, but it need not get in the way of anything.
If that religious belief leads you to make a public decision on public policy, however, and it's something I disagree with--ie, being anti-gay activism, being anti-Israel, supporting the teaching of intelligent design over evolution (I have friends who'd fit all three of these descriptions)--then it becomes more my business. It need not end the friendship, though, even then, unless it's something which is extremely egregious--again, you can be respectfully anti-Israel the same way I'm no fan of Iranian politicians, but if you side with, say, Hezbollah and Hamas and argue Jews in general should die, we're gonna have a pretty short friendship.
Your personal values may conflict with mine, but if they conflict to the extent that they wish to extinguish or destroy mine or those like me, then THAT is the step too far.