Pedantery ahoy, but I'll take your question at face value.

There is no such term, as nobody is a whataboutist. Whataboutism is a rhethoric tool.

While some rhethoric tools are always used intentionally, like jaq-ing and concern trolling. some are frequently (far from always!) used unconsciously because they just feel right:

Attack on character, sealioning, whataboutism, appeal to authority, argument to moderation, fallacy of the beard, false dilemma, false equivalence, kettle logic, et cetera.

In my experience, the answer to your question is "usually not".

I doubt it, particularly because it's almost certainly the case that the people who deride it when others do it do it themselves in other situations.

It's far and away most common in partisan politics, and it happens because the simple fact of the matter is that most professional politicians and political parties are loathsome slimeballs, and the only thing a partisan can dependably say in support of their preferences is that they're (purportedly) better than the alternative. So it's nearly always the case that in attempting to defend or advocate for their preference, they'll bring up the alternative and shift focus to them.

And then they'll potentially turn right around and deride their opponents for doing the same.

Some do; others think it’s a valid argument because they see their media sources (or at least people around them) do it.

I think that some do, some don't.

Some people who use the fallacy (it's a type of red herring) show signs of knowing that it's logically invalid, and that they're still doing it because they value persuasion over moral/intellectual standards. But in some cases it smells a lot like plain lack of rational thinking.

What about a whataboitist that’s in fact a she? Or, like “they”

Yeah I thought so.

(/s)

Please keep all replies on topic. People should be able to have a discussion about the term without devolving into personal attacks.