Loomer also has a right to sue them for defamation when Facebook uses it's arbitrary definition of "hate."
No she doesn't. Legally, Loomer doesn't have a leg to stand on here. Facebook can make any sort of artbitrary decision they like to ban a person, and they don't have to justify their reasons. It's a private company. They can't ban her on race, religion or nation of origin, but that's about it. The usual "public accommodations" stuff.
Look at it this way. You invite someone to your home for a dinner party. The guests are a diverse group, but one of your guests comes in, and starts calling people racists names, acting like a total asshole, insulting and offending your other guests, and arguments are breaking out.
Are you going to stand there and say "She is just expressing her opinions as is her right under the Constitution", or are you going to say "You can't talk like that to my other guests. Stop it right now or you'll have to leave".
The right to "free speech" in America is not a carte blanche to promote hate and bigotry. The right to "free speech" is extremely limited: You cannot be arrested or prosecuted for criticizing the government. That's it. You cannot enter a private business and start shouting that you hate brown people. They'll throw you out and rightfully so.