How does one even begin to deal with this level of stupid?
Easy. You filter out early. People do this for schools man in putting the best students in the top class, at an age when the kids haven't even figured out why it's important. Goes without saying for well run companies, where background checks are fairly thorough to assess character, and probationary periods go on longer than what's officially stated.
Yet for picking the people that are to impact the fate of all of us in their decisions, the biggest filter-requiring situation of all, you just let them through. It's pathetic.
You can't filter for character through a written test, but if your political leader is going to be a poisonous c*nt, he / she can be a competent for the relevant fields, poisonous c*nt at minimum. That you can work with, till you can improve on him / her.
The Trump / Greene level of garbage is irredeemable, you can only improve by removing it.
Make all of them pass exams on areas, subjects relevant to a management of a country, administered by an independent body every few years, based on the election cycle. Idiots like this one, Trump get filtered out.
I would do the same for voters, heavily, life changing-ly incentivised, and make voting (ie undertaking that exam, and to vote if you pass) compulsory.
The solution is clear, you simply don't hear of the will to make it happen. You don't have a filtering mechanism for both nominee and voter, every few years you're open to insane, unnecessary volatility. It's great for markets, for people looking for opportunities but you really don't need to risk the futures of the general population by leaving the door open for garbage that lacks the basic mental level.