Looking at his public statements about women I think it's clear he is a misogynist but mainly in his personal dealings. It's not really a feature of his politics.
As for racism I think the Muslim Ban was a clear case of explicitly racist policy.
Looking at his tendency to switch wives for a newer model is clear evidence that he has a lack of respect for the women in his life. But there is little evidence that his policy positions disadvantage women.
The travel ban was not something I see as racist. It was nationalistic and popularist. There was a terror threat and Trump actioned a broad travel ban to make his voters feel protected from that threat. Did it actually protect anyone, probably not. Did it unfairly disadvantage huge numbers of primarily Muslim people, yes it did. But the intent had nothing to do with them being Muslim, it had to do with their perceived link to terrorism. You could argue that it was racist to ignore the rights of all these foreign nationals but I think Trump's position was that he only cared about Americans. He was a strong nationalist but in my opinion not a racist.
But there is a correlation wrt race and religion, so how do you distinguish?
Most neo-Nazis and white supremist are white, isn't any action targeting those groups also racist? of course not; but what's the difference between that argument and the so-called "muslim ban"?
I don't really distinguish, there are technical differences but it's not as though one is ok and the other is not. Would a religion-ist ban really be any more acceptable? Either you accept that each person should be treated equally as individuals irrespective of such characteristics, or you don't.
Neo-Nazis are not targeted under the law for being Neo-Nazis. They are targeted for individual criminal acts they perform personally, or conspire to perform together. Some small groups have been outlawed in some countries, but only in the same way that criminal gangs such as the Mafia or other terrorist organisations are targeted. That is in no way comparable to targeting "Muslims".
The mistake you are making is to conflate the criminal act with the motivation for that act. Setting a bomb or shooting someone because you are a Neo-Nazi does not mean that if someone prosecutes you they are doing so because you are a Neo-Nazi. They are doing it because of the bomb or the shooting.
This is the mistake the MAGA crowd on the Capitol were making when they were surprised and shocked that the police didn't come over to their side. It's a characteristic of racism that it conflates group identity with individual identity, and it's also why I am vehemently opposed to far left identity politics which makes exactly the same mistake.
They may be on opposite sides of the political spectrum, but wing nuts generally are susceptible to the same cognitive failure modes.
> Would a religion-ist ban really be any more acceptable?
I don't really see religion as any more than personal/group belief; I understand America sees it differently, and privileges religious belief.
Is a religion-based ban more acceptable? yes, race is an immutable characteristic that does not determine or prescribe a persons actions or motivations - "religion" is a systems of belief that absolutely does.
> Neo-Nazis are not targeted under the law for being Neo-Nazis
If the metric for hate speech is guilt-by-association with acts of violence, any ideology that promotes violence is hate speech. Neo-Nazi ideology falls under this category, and I believe "refusing entry" has a lower bar then outright bans on freedom of expression.
> That is in no way comparable to targeting "Muslims"
The Muslim ban was so-called by Trumps opponents. The ban targeted specific countries, and was not an exhaustive list of all Muslim nations.
> The mistake you are making is to conflate the criminal act with the motivation for that act
I'm not sure they are so different. Thought-policing ones own citizens is chilling, but I'm less certain about doing the same to refuse entry - we already filter based on a persons character.
>The Muslim ban was so-called by Trumps opponents.
Er, and Trump himself. Many times. It was really important to him that people understood that. He explicitly and frequently said it was his attempt to implement the explicit Muslim ban he promised in the campaign.
I agree religion is a choice, but 'Muslim' is simply a massively broad category. It includes many groups that are implacable ideological and religious opponents of each other, and says practically nothing about a person's actual likely behaviour or actions. As with all racism and other-ism the belief otherwise is nonsense on stilts.
As for racism I think the Muslim Ban was a clear case of explicitly racist policy.