How about teaching students not what to think, but how to think? Essentially analyzing claims to determine validity; examining not just the answer and how we came up to it but also the question itself. The best teachers I had didn't just teach the answers, but they taught us how we came to them and why, so maybe classes regardless of topic should include this sort of reasoning and analysis instead of just what is "right" and wrong.
Maybe a political science class(es) would be a good addition alongside a general education regardless of what career a student would eventually take, and maybe a class that introduces students to the different ideological or religious views designed and taught by those views who want to teach, not proselytize or indoctrinate, students about their believes.
The reason I'd suggest a introduction course is that I think with excluding any official teaching on those ideals and leaving it to families who may not know or fully understand them, is that they might present a false representation based on biases. Asgardia will most likely be a nation of many different ideals, and allowing potentially biased and incorrect understanding of those ideals to permeate through the society, I think would be a bad idea. We only need to look now at the many situations around the world where certain groups are demonized, many because people have this misinformed idea about those groups that's been allowed to spread unchecked and unchallenged. We should be open to exploring them, regardless of how comfortable we might feel if only to prevent further stigmatization against them.
I'll take the idea of Evolution since it's already been dropped: it's hard to study several fields in biology without acknowledging the certain mechanics of evolution coming into play. So while its studied in science classes, we should also have class that examines the controversy surrounding the topic of evolution and examine why we have them.
This is a pretty interesting subject, thanks for bringing it up, I look forward to responses and continuing the discussion