I presume you mean "in a government school", in private schools the matter is completely different. Also, any administrator is free to express their wishes, the salient question is what command can be enforced.
If the state enacts a policy rule for education, that rule is therefore enforceable against an employee. If the state does not enact such a rule, the district still has the option to set its own policy, as long as it doesn't contradict existing law and constitutional rights. The same reasoning carries through to the relationship between district policy and the policy of a specific school. Your boss can tell you what you do, even if the bosses boss didn't make such an order.
The guiding principle here is that your superiors are allowed to state what the curriculum is, and to the extent that they haven't said anything on a topic, you can express yourself freely. When they tell you that you cannot exclusively teach the MAGA theory of modern American politics, then you run a risk of sanction. There are political and legal means of challenging those sanctions, the latter of which would rely on the First Amendment, that is, the government cannot prevent you from expressing your political opinion. On the other hand, the government is also not obligated to provide a paid platform with a captive audience for you to express your opinions. This is why you cannot preach a religion at your students, or require them to (at least superficially) accept a particular political ideology – that violates the rights of students.
If there is a state law requiring the teaching of some particular matter, then you must teach it, because the state commands the district, and the district commands the principal who commands the department head. If the state is silent, but the district has a policy, that gives you a different starting point but a nearly same result for the individual teacher. When rules are added at the lowest end of the chain, there is a significant chance that the immediate superior actually does not have the authority to make such a rule, and does not have enforcement authority. The district almost certainly has authority to set policy, but it's not so obvious with principals and department heads (look at your contract).