It's tricky. They are certainly used in slur-like ways these days. I would say the difference is that white supremacist and racist are pre-existing terms that are widely considered to be neutral descriptive terms. You can use neutral terms in non-neutral ways and over time they may start to take on the slur connotation. But I don't think we are there yet with the established terms.

Is there a way to express distaste for racists that doesn't use the word like a slur?

I'm wondering to what extent statements like "racist is a slur" is equivalent to "people frequently express distaste for racists"

You can certainly be explicit about the negative evaluation, e.g. "racism sucks", "being a racist is not cool". The issue with language is that context imbues words with meaning. So when you use a term in such a way that the dynamics between the term and the context leads to associating the negative connotation of the context to the word itself, further usages of the word then carries that negative connotation with it. In the case of slurs, they no longer (or never did) carry any neutral meaning. So the difference between expressing distaste and using a slur is how the negative connotation is expressed.