I agree with the guy in the video when he says that no student should be able to tell the political leanings of their teacher. That is crucial.
I also agree with IM2 and others who point out that it is school's job to teach the students about politics. School is where they learn what liberal and conservative, left- and right-wing, socialism and capitalism, Democrat and Republican, democracy and autocracy, and so on all mean. In order to do that, the teacher needs to be able to say "Liberals believe this" and "Conservatives believe this," and so on. So they have to talk about it.
School also must teach how to identify bias, fallacies, hidden agendas, statistical manipulation, confirmation bias, echo chambers, appeal to emotion, and a bombardment of other manipulations that the students absolutely will encoutner once they join the electorate. This has never been more apparent than it is now.
Which is where Video Guy's basic mistake comes. He thinks that the teacher including that cartoon demonstrates that the teacher had an anti-Trump bias. It does not. Political cartoons have played a central role in our electoral system dating back to the beginning, and to avoid showing a contemporary example would be leaving a big hole in the curriculum.
Good teachers have the ability to present information without endorsing it, and it sounds like this teacher made it very clear that that is what they were doing. It doesn't seem like Video Guy thinks that way, though. Also, he's a random guy on his own YouTube channel. He is under no obligation to present the full story; there is no reason to think the teacher didn't also circulate a Biden cartoon, which Video Guy simply ignored.
Without any actual evidence, I don't think the teacher has much to worry about, except of course to have an argumentative helicopter parent making their life more difficult.