"Liberal," at least on Lemmy, has become more or less a meaningless word. Any word that has so many definitions, different depending on who you talk to, it becomes sort of corrupted and useless.
I've literally seen several times a conversation generally of the format "You support Israel!" "wtf no I don't" "Yes you do because you're a liberal and I know that because (whatever)! You're lying, you support Israel! All liberals support Israel!" I'm exaggerating slightly but that's the basic core of it.
Interestingly enough, the proto-MAGA movement was trying for years to turn "liberal" into a slur before the internet turbo-leftists got in on it. It basically fulfills exactly the same function in both cases: Just a checkbox that means "enemy" which can be used to shut down critical engagement, because humans have an instinctual category for "enemy of the tribe" for which engagement is meaningless, and you just need to attack.
IDK what word you could use to refer to news like MSNBC. I actually don't see a problem with saying "liberal" to mean news like MSNBC / The Atlantic / similar points on the spectrum, but on Lemmy, you're going to really get people confused. The word in general is just best left avoided I think.