I despise McCoy for example, I understand he's supposed to be the emotional one of the main trio but being emotional doesn't mean you have to act like a racist hick
He doesn't act like a racist hick at all. McCoy is awesome and the heart
of the trio. As for his barbs against Spock, it was banter and Spock gave back as good as he got (which was actually very popular at the time. Fans wrote in and wanted more of it). Okay sometimes they argued for real but deep down McCoy and Spock cared about and respected each other. Their relationship was the typical "I can't admit that I like you". But I digress;
Anyways the above is the perfect example that some fans can't look at things from the context of when it was written. They judge the writing, characters, and special effects from today's standards.
They don't understand that the things they watch today will probably be considered politically incorrect, cheesy, and dated in 40+ years too.
Normally I wouldn't use TV tropes as an example but I think this is the perfect one to describe negative reaction against the original Star Trek