Since the definitions no longer mean what they originally meant, new launguage is needed to distinguish old from new. Also to help avoid confusion and accusations of prejudice and bigotry.
The problem with trying to come up with new terms for these guys, that "avoid ... accusations of prejudice and bigotry", is that any new term we come up with will, in very short time, come to have all the same negative connotations that the current terms have, because the people we're describing really do show all the negative attributes implied by the term.
We saw this happen, in real time, right here on this forum, with regard to the term "Truther" as applied to the 9/11 brand of conspiracy theorists. This was a name they came up with themselves, and proudly used, because (at the time) it made them sound good - who wouldn't be in favor of finding out the truth?
But within a just a couple of years, "Truther" became an at-best ironic misnomer, and a few years after that, Truthers themselves were rejecting the name, claiming it to be a pejorative that non-Truthers applied to the CT crowd, in order to mock, belittle and oppress them.
And that transformation all happened not because of how WE used the term, but solely because of how THEY behaved.
And that will happen to any other term you could suggest we use.
Go ahead, try it. Come up with a name you think isn't subject to "confusion and accusations of prejudice and bigotry", and I'll bet you that, if it becomes popular, within 5 years, it will be considered to have most or all of the negative connotations that Truther and Conspiracy Theorist have now.