In Star Trek The Original Series, there was one episode in which Dr. McCoy (??) called Mr. Spock a "half-caste" or a "half-breed". I don't remember which episode it was, and googling "Memory Alpha, Mr. Spock, half-caste" would require that I read the entire scripts of several episodes, of which This Side of Paradise looks the most promising.
I am more interested in the viewer reaction, if any, to this term which today would be regarded as highly offensive. I saw The Original Series when it first aired (1966) and even then I was startled by the use of this term.
It would be a bonus to know in what episode this occurred, but the question is about the viewer reaction, or lack or reaction, to the use of this term. If there was no reaction, could the context have made the term excusable?
Addendum In reading the link provided by @Valorum, it was Kirk and Scotty who called Spock a half-breed, not McCoy, and, from the short excerpts in the link, it seems that they were not in their right minds when they did.