If you had red hair, would having red hair be part of your identity? It might, but I'd guess that it wouldn't necessarily be a big part of your identity. If you were one of relatively few people in an environment who had red hair, I imagine that having red hair might be a bit more important part of your identity. But even then, I wouldn't guess that it would be a large part. But what if others treated you differently because of your red hair? If this was the case, having red hair might be a much more important part of your identity. And if other people treated you not just differently but poorly (i.e., treated you worse than they treated others with different hair colors) because you had red hair, then I imagine that it would be an even more important aspect of your identity.
This is not too different from how I think about atheism. Atheism is part of my identity, but it is not a very large part of my identity. If I wasn't surrounded by religious believers, it would be a smaller part. I suspect that if I were to move from Mississippi to Vermont, a far less religious state, I'd quickly find that atheism was a less important part of my identity. I'd probably think about it far less than I do now. But most of all, if I wasn't treated differently because I'm an atheist, it would be a much smaller part of my identity.
The fact that I don't believe in gods puts me at odds with the vast majority of my neighbors on something they seem to consider to be extremely important. And when they find out that I disagree with them on this issue, few react positively. I can usually set aside the threats of hell since I don't believe in it either, and I sometimes find myself feeling sorry for those who choose to go that direction. What's harder is when I run into the conviction that I cannot be a good person because I don't believe in their god(s). This one is harder because this belief seems to influence how they treat me. No matter what I do, I'm going to be that person who can't be trusted because I'm an atheist.
So why is atheism a part of my identity at all? Because it leads others to treat me poorly. If they didn't, I'm not sure I'd give it much thought. I wouldn't need to do so.
