Private schools can mostly do as they wish. Government schools have to follow constitutional provisions that pertain to government action. The most basic relevant principle is the Equal Protection Clause, which forbids a state from denying a person the equal protection of its laws. The government cannot limit First Amendment rights to one group, because they espouse a viewpoint that isn't in line with the ruling party's beliefs. The law is to be enforced in a viewpoint-neutral fashion, not selectively (e.g. Good News Club v. Milford High, Cornelius v. NAACP Legal Defense, Dwares v. New York).
This does not mean that a policy, once stated, must always be enforced. School districts typically have policies defining unexcused absences and penalizing students for having too many of them. These policies are usually indirectly or directly compelled by state law, such as RCW 28A.225.010. This law even-handedly allows all religious excuses, and no political ones. Again, it is not required that unexcused absences for political reasons always be punished. But the decision to punish cannot be based on the particular viewpoint being expressed. If a district generally does rigorously punish political absences for right-leaning causes, it cannot rigorously ignore political absences for left-leaning causes.