Yes, certainly there are some atheists who are "religious" about it, and will vehemently teach their children that there is no possibility of any deities or afterlife, and that anyone who tries to tell them otherwise is mentally defective somehow. But I would agree that's just as tragic as indoctrinating someone into any religion, and that certainly isn't the only kind of atheist. But if you're going to be a part of your religion, and teach your children to believe in it, that's always going to be some degree of indoctrination.
I do really appreciate parents who are religious, but do their best to let their kids find their own way. I suspect that's a much rarer phenomenon than the atheist parents who do the same, though.
Let's also not get into an atheist vs. agnostic debate. My take on it is that if you are not agnostic, at best, you're a "religious atheist" who presents belief (that there are no deities) as fact, and that's just as dishonest as teaching someone the "fact" of a god and heaven and hell (or whatever).
From what I understand, you would say that my mother was indoctrinated and I wasn't, despite both of us growing up in nearly identical households with parents who had the same spread of opinions. This seems like an obvious double standard to me.
She's religious because her school had really good religious role models who taught Mendelian genetics and seemed like respectable adults, and I'm an atheist because I grew up in the Richard Dawkins vs creationism slapfight and didn't get a good impression of religious people during it. It's got nothing to do with indoctrination. Her religious education was arguably less of an indoctrination, since mine was administered by Access Ministries and wasn't particularly nuanced, while hers involved something pretty close to comparative theology.
I don't have a good handle on what's more common on the atheist side: indoctrination into the "be against religion at all costs" camp, or the "we don't believe in that stuff, but we're happy to answer questions and help you find answers and learn about religion if you want to" camp (the latter of which I certainly wouldn't classify as indoctrination).
My hope is that the latter type of atheist family is more common. But that may just be naive wishful thinking.
But I think your situation, with one atheist parent and one theist parent (and same for one set of grandparents), is likely less common than all three categories above. And I would also expect that your mother's situation, where she was introduced to religion during early school years and allowed to make up her own mind, isn't all that common either. But even then, I question how much she really got to make up her own mind. I suspect if she had attended a secular school with no religious role models, she may would have ended up an atheist.
I think the point I'm trying to get across is that I think agnostic atheism is generally born out of a lack of indoctrination. Both theism and strong atheism usually come from being indoctrinated into that sort of thing. The fact that your family is different -- and IMHO fairly rare -- doesn't really invalidate that. It just means there are exceptions, which... well... welcome to our messy universe, where precious little is absolute.
Not to downplay the fact that indoctrination does frequently happen. I just don't think it always happens, and exceptions seem to be quite common for the people around me, though I don't live in the US.
No, the main non-agnostic atheist belief is "The current religions are bullshit" which there is plenty of evidence for, so it is a much more rational belief than belief in any religion. Therefore it can't be classified as a religion since there are strong rational arguments behind it.
Also you don't need to be agnostic or non-agnostic, or even an atheist, to believe that the current religions are bullshit.
I'll never again outsource my morality.
Most often people exhibit bounded rationality, as "completeness" is a heavy cognitive burden and transitivity is hard on the margins.
Neither components of rationality require belief, and both recognize that choices (free will) can be made, suggesting more nuance to your argument is needed.
One can simply observe vehement followers of conflicting religions to determine that someone must be wrong, and it’s more likely that everyone is wrong than not.
But yes, this is the thing that always gets me. It takes a mind-blowing amount of arrogance to believe that your religion -- out of all the thousands that currently or used to be practiced -- is the right one, and everyone else -- billions of people -- just absolutely must be wrong.
And if you don't have that arrogance (but are nonetheless religious), the only reasonable stance to take is that you believe there is a god, or many gods, or perhaps some sort of supernatural universal force; and that there is maybe (but maybe not) some kind of afterlife, or reincarnation system, or... who knows. But I meet precious few religious people who think like this; I guess most people who fall into this category would tick the "spiritual, but not affiliated with a religion" box.
What if that deity has made itself directly known to, and has had direct contact with, humankind?