In practice, people have trouble not butting into each other's lives. If we're going to try to force a shared belief on everyone, it should be to fix that.
There's a lot to be said for giving all children a baseline level of education based on fact so that everyone understands the world and the large problems we have and so they will know how to work together to face them.
The kids who are only ever taught that the world is 6,000 years old and flat, that women are inferior, that evolution is a lie, that global warming isn't real, or that gay people cause hurricanes are going to be at a substantial disadvantage in many areas of their lives and they will hinder efforts to resolve conflicts, to coordinate when necessary, and to reach general consensus.
And what if I want my kids to go to a school where they’re encouraged to think for themselves? To be interestingly wrong rather than boringly correct?
I really don’t think the facts you give as examples are that important when it comes to equipping a child with the skills they need for a lifetime. They’ll be faced with a different set of facts later in life anyways. The foundation of an education needs to be a little deeper than “not my enemy’s political views.”
Sure it could make politics more polarized, but hopefully that will result in greater diversity of governments under which one can choose to live. Anything that gets us away from a monoculture and a single world-government is a good thing in my mind.
The social aspect of schooling is just as important as the educational part of it. There's a reason growing up when we had home schooled kids that joined for their high school years, they were the "weird kids" - they just had absolutely no idea how to interact socially with their peers. And for some folks that carries on to adulthood.
Disclaimer: my parents were public school teachers, and seeing the system deteriorate feels like a travesty. The number of parents who think school is daycare is disheartening to say the least.