I think just being honest is always best.

My parents got a double whammy... I came out as both gay and atheist at the same time. Strangely they were a lot more concerned about my being gay than my being atheist. I came out also as atheist in order to take away all their religious arguments about my being gay. It worked in the sense that they had no arguments outside fo religion.

They eventually came to terms with both before they passed on.

I am sorry that I do not believe as you do regarding religion I believe only in that which is supported by facts that can be backed up by science. They still will not like it.

If they care about you just be straightforward. It won’t matter. When my son came out as gay(I always knew he would be an atheist) at 13, we just said and...
We told him we loved him no matter what.

If you love them then they must be loving. In which case you shouldn't feel any anxiety about coming out.

Thats tough on what your mother said. We all have to make our own path in this life. Good on you for choosing what is right for you.

Honesty is always a good default position. But start where they are at. Some ideas are: Talk about your central concerns and values in life, then maybe introduce a few religious tenets that, if taken literally, are problematic. Try separating the issues of belief in God from scripture as definitely man-made and not infallible and that from the question of religious organizations being human organizations, not the mouthpieces of god they claim to be. Let them hear how much careful thought you've given the matter and that it is NOT laziness or rebellion motivating you. Then get ready for dialogue. My dad is 80 and still can't deal fully with my atheism or me being gay. The atheism scares him more. And his Bible clearly tells him it is his absolute duty to "witness" to me, so there you have it. They either respect our non-belief (and tacitly admit fundamentalist approach doesn't work) OR they fulfill their duty to witness and not "give up" on our "salvation." It isn't possible to have it both ways.

I take it you're meaning atheism not gay? It probably doesn't matter, should be same either way. I'll bet your family suspects in any case. Personally I just came out and told them. Life is short. It feels so much better to be up front and truthful. My parents were very religious. I just avoided letting them know. I regret not letting them know who I am. I think I owed them that even if it brings an uncomfortable response. Now it's too late.

I honestly don't know, but Hemant Mehta has a video that might help you. Same for Theramin Trees.

My family has always been extremely liberal allies. First when I came out as pansexual I said "mom, dad, I don't care what is in someone's pants, but rather in their hearts" and it was actually really underwhelming. 'Uh yeah, that's how you're SUPPOSED to love someone'.

Then when I discovered I'm actually asexual, my dad was like "meh" my mom however...gosh "you just haven't had the right sex, it must be a trauma causing mental issues around it, maybe you have low hormone count, have you considered seeing a sex therapist? I just don't understand how this could happen to a child of mine. You would be better off not talking about it and just have sex even if you don't like it, no man wants a prude, oh my poor broken child"....