Why would we want to to respect anti-LGBT people?
The fact that I even need to answer this is proof that this is something our society needs.
Basically it boils down to being respectful of people even if they have views that differ from yours.
It is my understanding that Star Trek leans more towards a future where people work together despite their difference rather than people being punished for for their differences.
Curios_Gelatin said:
Would it have been a better idea to have someone on the show disapproving of Uhura because her skin was a different colour?
I think it could have been advantageous to have to show that a racist a person of a race different than them being able to work together. It's that a good message to send that: Yes, we disagree but we can still be respectful.
Perhaps have a xenophobe and an alien on the same crew.
I think show that people can be civil even when they have vast differences is incredibly more hopeful than labeling people who you(general not you specifically) disagree with as bigots or hateful and shaming them out of existence.
IDIC, tolerance, etc. can't be one sided. If we can't be tolerant of people who disagree with or even dislike us, then we really aren't being tolerant.