I had regular debates with him but he graded me well because the papers I wrote were clear, concise, and well documented.
If your daughter is willing to risk a bad grade, she should turn in a paper that successfully undercuts the leftist nonsense of the teacher.
If he is a decent person he will grade her properly. If not, she should try and drop the class without penalty. The one thing about liberal administrations is that they don't want their precious students or the parents of their precious students to be embarrassed by bad grades. So they tend to make it rather easy to drop classes without penalty and without the class ever appearing on the students' transcripts.
She should do something early in the quarter/semester to challenge the teacher in a respectful manner to see how he reacts.
If she absolutely has to take and pass the course, then she could pretend to be even more left than the professor. Basically espouse doctrinaire Leninist dogma which requires the dictatorship of the proletariat. This will confuse the heck out of the professor as he has to argue with her from the right.
Don't do it. These are not decent people.