There was a book about authoritarian personalities I was reading a while ago that was fascinating and depressing. It had a study that showed right wing authoritarians are also willing to hunt down themselves

From this book https://theauthoritarians.org/

Suppose the federal government, some time in the future, passed a law outlawing various religious cults. Government officials then stated that the law would only be effective if it were vigorously enforced at the local level and appealed to everyone to aid in the fight against these cults.

[...]

Who can ’em be? Nearly everybody, it turns out. I started with a proposition to outlaw Communists and found authoritarian followers would be relatively likely to join that posse. Ditto for persecuting homosexuals, and ditto for religious cults, “radicals” and journalists the government did not like. So I tried to organize a posse that liberals would join, to go after the Ku Klux Klan. But high RWAs crowded out everyone else for that job too. Then I offered as targets the very right-wing Canadian Social Credit Party, the Confederation of Regions Party, and the mainstream Progressive Conservative Party of Canada. These were the parties of choice for most authoritarian followers at the time, yet high RWAs proved more willing to persecute even the movements they liked than did others.

Finally, just to take this to its ludicrous extreme, I asked for reactions to a “law to eliminate right-wing authoritarians.” (I told the subjects that right-wing authoritarians are people who are so submissive to authority, so aggressive in the name of authority, and so conventional that they may pose a threat to democratic rule.) RWA scale scores did not connect as solidly with joining this posse as they had in the other cases. Surely some of the high RWAs realized that if they supported this law, they were being the very pople whom the law would persecute, and the posse should therefore put itself in jail. But not all of them realized this, for authoritarian followers still favored, more than others did, a law to persecute themselves. You can almost hear the circuits clanking shut in their brains: “If the government says these people are dangerous, then they’ve got to be stopped.”

So I wouldn't bank on their self awareness

May I introduce you to The Alt-Right Playbook

TL;DR: they absolutely do not care.

There is only one party that cares about hypocrisy. And it ain't the conservatives.