The biggest is that he believes in the many-worlds alternative to quantum mechanics. This is a belief that anything is possible, and that nothing is more likely than anything. It is a complete rejection of all modern science.
He has his own rationalization that is mostly circular reasoning.
In his latest Ask Me Anything podcast, he says that he does not see a moral justification for parents spending money on their children's education. He says all children should get the same education.
He is married with no kids.
He is welcome to his opinions, but he does not describe the American situation accurately. In California, his home state until recently, the schools get about 50% of the state budget, and the poor districts get at least as much as the rich districts. The rich are not getting any better educational opportunities.
Some rich parents do send their kids to expensive schools, but the educational opportunities are not much different from public schools.
He has also joined the sex-deniers who say that biological sex is not binary. Biology professor Jerry Coyne is a big fan of Carroll, because of what he says in favor of determinism and against libertarian free will, but schools him on biological sex.
In reality, what they are trying to do is the reverse: adjust scientific reality so that it aligns with social justice. That is, if sex is a spectrum and not binary, then people of different genders can somehow feel that they are in harmony with biological reality. But that’s an example of the “appeal to nature.” The rights of people of different genders, including transsexual people, do not depend on the developmental biology of sex, or of any observations in nature about sex dichotomies.Carroll is not a biologist. He is not to be confused with the somewhat more accomplished scientist, Sean B. Carroll, who really is an expert biologist.
I’m not going to discuss my claim that sex is binary; I’ve talked about it at length, as did Luana Maroja in her piece at Substack. I’ll just put it out there that the going biological definition of sex is that there are two sexes in vertebrates: males (who produce small mobile gametes) and females (who produce large, immobile gametes). There is no group that produces intermediate types of gametes that can unite with other gametes, so there is nothing beyond these two sexes.
I assume that Sean M. Carroll is smart enough to know the difference between male and female. But it appears that he is willing to recite nonsense in order to please his Leftist Woke fans.
I suggest keeping this in mind when listening to him. He sometimes gives pretty good explanations of textbook physics, but his opinions on big picture physics are dubious, and his moral and politcal opinions are garbage.