I don't have kids, so can't really answer the poll.
And none *quite* fit me or what I would do for my kids.
Appreciating your ancestors and your culture is more important to me than religion, per se, although religious traditions are often a part of culture.
I'm Native American, and was more or less raised Zuni religiously, and try to still attend our religious dances and traditions whenever I'm in Zuni. There was never really a big emphasis on belief or anything like that, growing up though. More importantly, it's part of our culture and traditions.
In raising my future kids, I would also raise them to appreciate their culture. Belief isn't so important to me, as much as is respect for where they come from, and their ancestors, and their traditions. Spiritually, they can believe whatever they want, but I'd raise them in their culture and mine.
Of course, this is made more complicated by the fact that I plan to adopt, so my children will very likely not be Zuni by blood. I would like to raise them in both cultures.
Native American tribes have always had a tradition of adopting outsiders to become part of the tribe, so I would still raise them Zuni, although they could not be tribally enrolled due to blood quantum policies (1/4 for us). They could still participate in the religion, and I would expect them to participate in some parts of it, at least.
I would also want to raise them according to their ancestral culture, whatever that may be, which would likely include religious traditions from their culture. All of which would be a learning experience for me, as well, of course.
I'd want to learn to speak and raise them to speak their ancestral native language, too. My mother never spoke to me in Zuni enough, so I still don't speak my native language. I want my kids to have their native languages as their first languages.
What my children believe spiritually is up to them, but I would raise them to appreciate their culture, including their culture's religious traditions and practices, regardless of belief.