asimov was a liberal jew operating in boston, but he was also an american with ideological roots in the progressive movement, which is where hitler's racial hygiene ideas originated from. that's a point glossed over by history - the theory of the master race was invented at stanford by progressives, not in some dank basement by nietzsche, who was thinking of something else, entirely.
so, asimov is a hydra on eugenics, for that reason - he is both a jew living through world war two and a period progressive.
in strict terms, eugenics means improvement of the human genome, and if you interpret that literally, it's hard to be overly critical of the idea. it's when you look at specific applications that the idea gets controversial, but you have to realize that there's a pretty good argument that wiping out the jews - who tend to actually be pretty smart - isn't much of an improvement at all, but rather actually kind of a bad idea. further, what we know about genetics nowadays is that race and intelligence aren't correlated. at all. in fact, race doesn't even exist as a definable concept, from a genetic standpoint - it's an irrelevant allele, in any meaningful sense. it's, like, three genes, and what it codes for is pretty unimportant.
but, then you look at things like autism (or tay-sachs) and you end up with a set of more complicated questions to ponder. asimov is generally critical of the sorts of ideas that you hear from advocates of eugenics, but he leaves open a lot of questions about potential legitimate applications of eugenics that genuinely reflects the state of the science at the time. if you don't actually know what autism even is, how can you suggest a solution to it? so, he frequently presents these nazi-lite characters and broadly frames their views in a negative manner, but he very rarely outright condemns them. there's this subtlety there that makes you wonder what he's really thinking.
as stated above, i don't have an opposition to the basic premise of improving the human race, but i think we have to understand what that actually means before we try and act upon it. if you're concerned about science or literature, it should be clear that killing all of the jews would be a massive negation to the genome. it should also be clear that sterilizing africans isn't going to have the outcome that race theorists of the last century hypothesized that it might. we know today that autism can be inherited from autistic parents but is generally actually a random error in real time that isn't predictable ahead of fertilization - it's an example of the error rate in random mutations asserting itself in the process of evolution. but, there are things (like tay-sachs) that...yeah...we'd be better off deleting, and can probably actually succeed in deleting.
when asimov discusses eugenics, he does so frankly, with the intent of generating an open discussion, and while he isn't always clear in stating his disapproval of inappropriate uses, it's nonetheless obvious that he's only in support of the kind of eugenics that may eliminate conditions like tay-sachs, and isn't in favour of any scientifically unsound theories of racial supremacy.
but, as is so often the case, he frequently fails to develop the point enough, and he leaves himself open to unfair criticism as a result of it.