What kind of fallacy involved lying about your political affiliations or being dishonest

I’ve seen some white Supremest use this argument when called out for Racism. “I’m not a racist or a Nazi I support the welfare state and universal healthcare and I support gay marriage”.

This is effectively trying to deny an allegation by making irrelevant references to unrelated topics.

Example:

Chris: [obviously racist language]

Daisy: That's disgusting and racist. 

Chris: I'm not racist at all! I support gay marriage and all that progressive stuff?

Firstly, Daisy was calling out Chris for making a blatantly racist comment. He can't defend himself by saying he supports gay marriage, for example, because no one asked about it. To suggest that one cannot be racist because they have a progressive view on a topic unrelated to racism is a non sequitur. Second, if Chris is lying, then the implicit argument is even more fallacious.

Daisy shouldn't, in this case, get hung up on whether Chris is telling the truth or not. She should keep pressing him on his crass, racist comment. To allow herself to be distracted by the claim would make her complicit in fallacious reasoning, too.

This very strongly depends on the context, let me explain.

To clarify, Lying is not a logical fallacy, but just a factual error.

So if someone is being dishonest, just call them a liar and give a reason for it.

So if they just say, "I am a nazi" but seconds later imply things that a nazi doesn't believe but rather would oppose then this would just be a shift of their own narrative.

Knowing that they deflect being one thing for obvious reasons shouldn't be too confusing.