Teach them reason, logic, open-mindedness, love and tolerance. Atheism/agnosticism will take care of itself.

I chose the first choice, because no, it is not your business to parent or teach other people's children. My caveat is that, if the child asks what I believe, and they are old enough to understand and contemplate, or I should say mature enough, I will share with them what I believe. I will tone my language down. Like, not tell them that the bible is completely idiotic and I think people who actually believe it need their heads examined. But I will tell them that I don't believe in it, that I find it illogical and silly, and give specifics if they ask. I will also say, but you should make decisions on your own. Tell them I came to my decision after intense biblical study. Not by anybody else's standards. I've been an atheist for years before even trying to connect with others who share my non-belief.

Absolutely essential.

I absolutely agree that good parenting exposes children to multiple sides of issues, however, as a parent I would have been madder than hell if someone had attempted to parent my child. I think this is somewhat dependent of the age of the child, but I think this requires serious consideration.

It is MORAL to tell anybody the truth.

The first choice is wrong. It takes a village (world) to raise a child. If a child is being prepared to not understand reality, then that child will not be able to provide a positive contribution to the village, when an adult. I tell kids, "Some people do not think the bible stories are true."

I think there’s some nuance to be highlighted here. It’s not ok to “parent” someone else’s child without permission, but having open, honest dialogue with them about who you are and what you believe is not that. If your goal is to proselytize, then yes, I believe that’s crossing a line (that goes for any faith, or lack thereof). But you are under no obligation to hide who you are from anyone. I also believe that one should be honest about the consequences of hypothetical conversion, and you should be aware (which I’m sure you are) of any potential backlash that can come your way, even if you’ve done nothing wrong.
Me personally, I don’t believe one can be “converted” in any way to which they weren’t already predisposed. If you replace atheist/agnostic with LGBTQ for example, these principles are exactly the same. No one can be “turned” LGBTQ. They either are and haven’t fully realized it, or they aren’t. “Exposure” is not a catalyst of change, simply a window to view through and a mirror to reflect on.

I don't think you can 'teach atheism', you shouldn't feel guilty for sharing what you think and letting a child know that not believing in god is an option. I feel guilty at Christmas when I pretend Santa is real ?

What is teaching atheism?

Atheism is not a belief. It's a blank slate.

If they think they have the right to preach to my kid their religion, I have the right to teach their kids that there is no god. This only applies in countries that do not have a state controlled religion. I won't go into any other kind of country

Not directly. Start telling kids that god/s doesn't exist and you will be on a hiding to nothing.

Start by teaching critical thinking, examine how they can distinguish true from false, real from unreal. Build through easy stages - is Santa Clause real?How do we determine this? How do we check the evidence, how can we test for this? Try it with unicorns, pixies, ghosts and then gods.

Let them work things out for themselves.

Why not? I mean I'm on the fence with teaching other's kids something that the parents probably wouldn't want you to teach them, but kids are bombarded by messages from EVERYONE and EVERYTHING on tv, billboards, school, friends, etc etc etc. Why should atheism or agnosticism be singled out as the "bad thing"? Parents seem to be oblivious to politicians and companies advertising to their kids 24/7, but thinking critically and hearing other opinions is blasphemy? Lol

I'm actually living this situation...
I've met a few young teens who volunteer. They are both from (somewhat) religious families. They have both talked to me (together and individually) about God and Believing and have asked me what I believe. I told them. I didn't preach or tell them that their beliefs are wrong or stupid. I simply answered their question. As you might imagine, this brought on a number of other questions, which I also answered.
I made sure they understood that lots of people believe lots of things and that we (the world) won't always agree about everything. The important part was to be true to yourself. I encouraged them to keep asking questions, but to be careful who you talk with openly on this subject, that some folks may take offense. They know that I am proud of them for who they are, regardless of what church they follow or not. (secretly I'm even more proud that they keep asking these types of questions!)

If you can't teach both sides if the coin in the21st century, I think there is something fundamentally wrong.

Tough one. I'm not sure I'd talk to the child of a fundamentalist about religion. I think I'd be more likely to talk to a fundamentalist Christian child in the US than a fundamentalist Muslim child in the middle east.

If the child wouldn't be in danger for changing their beliefs, I'd absolutely talk to them if they wanted me to.

My answer is a switch of your title.
Is it ethical to teach religion to atheist children?

The religious do it because they don't want you to burn in hell. They are terrible.

For anyone (children included) to have a balanced opinion, whether it be on religion, politics, or flat Earth, all sides of the argument must be given, without it, ignorance will be the outcome.

What is "teaching" atheism?

With religion being a fundimental factor in almost every society, community, region, and government in the world. Why the hell does the one nation in the world that aspires to be the "Melting Pot", the champion of freedom, the opitomy of diversity fail miserably to teach theology in school? Not religious study, but world religion. Public school children should be encouraged to understand other religions so that they can both reinforce their beliefs at home as well as open healthy discussions about their different beliefs....

simply explain why you are agnostic without pushing that they choose the same. inform don't push

Yes, but remind them there are thousands of religions all over the world, and they think they are right as well...

would I try and convince someone else when I don't claim to know the truth