I agree with lots of what the lazy parents said, but their practice was shoddy. Letting your child make their own mistakes is not the same as not being there for them when they are sad or to keep them safe. I practice a lot of the same ideas but with kindness and proper safe guarding. They also shouldn't be cleaning up after them if they are taking responsibility (though I do find myself doing that a lot too!)
The feminist annoyed me because it wasn't feminist parenting. I am a feminist and a parent and that spills over into most of my children's toys being gender neutral. It doesn't need to be so extreme. You paint children's nails if they want them painted not because it's "girl stuff" but because it's something they enjoy. We don't have boy stuff and girl stuff, we have conversations about the difference between girls and boys anatomically in an age appropriate way, but do not relate those issues to their play or life goals. It's not contrived, it's just not rigidly conforming to gender stereotypes. And it doesn't have much to do with feminism really it's just an over spill from the real issues (discrimination, domestic violence, wage inequality, etc.)
I like the chess, martial arts and cookery lesson. They had some good ideas and it seemed to work well, initially I thought it was a bit controlled and the man was quite domineering, but seeing him have fun with the kids and how happy the wife seemed with it, I think it works well even if it wouldn't be for me (their relationship) I think their parenting was the best. I will be dusting off my chess set and limiting screen time a bit more, we already do cooking and karate. I especially liked where he spoke about the importance of letting kids have free time to be creative. I think we forget that a lot.
I do think these programs always focus on extremes when actually kids benefit more from a flexible approach. There is no reason to not have a gun free zone and do karate. To have no foods off limits, but also do healthy cooking with them. To encourage them to explore their gender but also know their sex. To let them have free reign in lots of ways, but also have appropriate safeguarding and boundaries. When you have more than one child it becomes apparent that what works for one doesn't always work for the other/s.