Appeal to (dis)respect

The common theme with the various examples of this response is that they deviate from the question "is this true?" and pivot towards "is this offensive [to me]?", which is of course answered in the affirmative. The offensiveness of the claim they are objecting to is then used to deny the truth of the claim.

Andy: There's no reason gay people shouldn't be able to donate blood.

Boris: There is a reason. According to statistics, gay and bisexual men in the US are significantly more likely to be infected with HIV.

Andy: That's homophobic.

Andy's response is the political correctness fallacy. It should be noted that Boris's response may also fall under the ecological fallacy if it is used to justify denying an individual the chance to give blood merely based on their membership in a category that's more likely to be infected with HIV.

Ciara: According to historians, George Washington was particularly unkind to his slaves.

Dean: That's not true, they're just trying to tarnish the reputations of the founding fathers.

Sounds like the ad hominem (circumstantial). The historians are predisposed to make the claim, therefore it is declared false.

Earl: OJ Simpson was found not guilty, so he didn't do it.

Fred: A not guilty verdict doesn't mean he didn't do it. In fact, a lot of the jurors thought he probably did it, but that there was reasonable doubt.

Earl: It's really disrespectful to the justice system to say the jurors didn't do their job correctly.

'Disrespect' has nothing to do with the truth of the claim. Also notice the strawman fallacy where Earl claims Fred suggested the jurors "didn't do their job correctly", which Fred never said.