Came out ftm to straight boyfriend

So, I came out to my boyfriend a while ago, maybe a month or two, I'm not good with passage of time at all really.. but at first he was really tentative and shit off as expected.
I let it slip, and he was confused and worried so at the end of the day I talked to him and he shut down almost. He definitely wasn't ready, and neither was I, but it had happened.
Now he's very supportive and he's calling me the correct pronouns, or trying to, and it's amazing. He's helping me as I get closer to inevitably telling my parents and I feel that it may happen sometime soon that I tell them.
But my boyfriend was raised very religiously and he was taught that it was wrong. He was taught it was wrong to be gay or to be trans or to be any part of lgbtq+, and I was very worried about it. He told me this and that while he had reservations, he would try to be supportive, and he's come a long way in this past month or two, again not good with passage of time. We've been dating for about 10 months almost and I had come out to myself during the midst of our relationship. He could tell something was wrong because I wouldn't talk to him about it, I would always call it a "me problem".
Now we go through it together and he helps a lot

 

I came out to my mom, it went half as well as i hoped. But heck yeah, I'm good with her. She told me not to rush into labeling myself, I know I haven't, but she supports me.