I really want to come out to one of my friends, she lives in the US and we chat online. I don't like her in that sort of way, we're just close friends and we share a lot. But she comes from a catholic family and although she doesn't talk about her religion I know some catholic people think badly of gay people. It's a big thing to keep from her so how do I mention it?
Not all Catholics are against LGBT people. Sure, some are, but they're mostly in the minority from my experiences. One of my closest friends is pretty religious and she has been nothing but kind and supportive to me. If your friend seems like the type of Christian that is nonjudgmental, go for it! Maybe if you can get on the topic of LGBT stuff, you can casually bring it up. That's how I would do it- casually. Don't make a big deal out of it, and she shouldn't make a big deal out of it. Good luck!
What Em said. Bringing up LGBT topics can be a good way to figure out where she stands. There are some horribly homophobic Catholics, but there are also some very open-minded Catholics, especially, in my experience, younger ones.
Hehe, coming from an ex~homophobic Catholic, perhaps you could ask them about their faith. It's a very diverse religion. Some are fire and brimstone, lots are more liberal in their interpretations. Perhaps getting a better feel for their faith will kinda guide how this friend will take to your coming out. I'm sure you'll do fine! The worst is that they try and tell you you're going to hell which isn't the case you can discuss it with them but hold firm to your own discovered truths!
^it is in no way certain that she will tell you you're going to hell.... Bringing up topics is a good idea.
If you want to, you should come out to her. It is part of who you are and you should not have to hide it. Be prepared that she may not take it well, but would you really want to be friends with someone who does not accept who you are?