I don’t have much to add that others haven’t said. I know it hurts, I’ve been through a couple really rough break-ups that hit me by surprise. The most important thing I can tell you, though, is that even though that sort of break-up makes the desire to “win her back” so overbearing that one is willing to do almost anything. But my biggest word of advice there is to stay true to yourself. It doesn’t really matter what you lost her to, but if you try to change who you are to fit what you think she wants or needs, you cannot recapture that magic that you remember. If you do change yourself, perhaps by becoming more involved in her beliefs, even if she takes you back, the entire dynamic of the relationship will have changed. And the worst part of that is she’ll then be interested in who you’re pretending to be and not who you are.
Also, really, try not to read too much into anything she might do. Starting a facebook or mobile game, maybe she just enjoyed doing those games with you, maybe she doesn’t want to just cut you out completely because you’ve broken up, maybe she accidentally invited you to the game, but I think it’s very extremely unlikely that it’s a sign she’s interested in getting back with you. I’d just say to do your best to take anything like that at face value, and if you want to play, do, and if you don’t or it’s too painful or confusing, don’t.
Ultimately, this is an opportunity to learn about yourself and grow, after you’ve taken the time to grieve. You can reflect back and see what went well, what didn’t, and take this time figure out what you want and need in the future. In my experience, support alone just isn’t enough, sometimes those passions have to be shared, and as others pointed out, even if you say now that it came off harsher than you meant it, I think that you didn’t share her passion for her beliefs, no amount of support changes that. It’s clear that it’s something that was important enough to her that she actually needs to share that. One thing I realized after a similarly painful break-up was, not only was my support of her passions just not enough, but I had actually been too willing to forgo the mutual passion I really needed for things that were important to me, and it led to friction, a lack of understanding, and a certain amount of resentment. I now realize that since these are things that are fundamentally important for me to share with a woman I’m dating, they should be for her too. So, perhaps some food for self-reflection is, what are these things for you? Were there things that, perhaps she supported as well as she could, but it just left you wanting her to really understand more?
Regardless, I know this is rough, and there’s no words that we can say to ease that pain, it sucks, but do know, you will get through it, and you can either let it drag you down or you can use it to turn out better on the other side. I hope it’s the latter.