If I were a professor, and a student came to me beforehand to request the opportunity to be able to make up a test or other work required in order to participate in a protest, I would of course take into consideration that student's performance in my class. I don't really mean the grade they are carrying, but more their attitude and work ethic. If they were a slacker, barely doing the work, and/or a disruptive or disrespectful student I might be less inclined to make allowances. But, the mere fact that they came to me beforehand to ask permission would carry a lot of weight in and of itself. It would also depend on what was planned for that day...a quiz would be easier to make up than a final exam, for example.
This makes a lot of sense - as you say a class quiz would be easier to make up and allowing an extra day to submit an assignment might be permissible. Rescheduling a major exam would be much less achievable, not least because of the possibility of other students giving advice on what the questions were going to be.
Someone requesting permission in advance and who is normally a good student could be granted some flexibility but it can only go so far. Re-reading the original question and the reference to "tests", if a test is merely a benchmark to see how well everybody is coping with the course so far (i.e. it has little to no impact on the final grade awarded) it arguably makes little difference if a student skips it completely (although that decision could come back with teeth if for some reason the student needs special consideration with regard to the final exam - perhaps due to an emergency - and their scores at informal tests end up being considered) but if it carries any weight at all then the scope to grant flexibility diminishes significantly.
In that regard I suppose it becomes like an employee requesting vacation time to attend a protest. If it can be done on the person's own time then it works but just like an employee couldn't expect special treatment when requesting vacation so a student can't expect special treatment either. Where an employee might be denied the time off, perhaps because it was the busiest time of year at work, so a student might be denied the opportunity to reschedule because the test was of significant importance. In that situation if they chose to attend the protest anyway they would need to be awarded a zero score in the test.
It reminds me of the story about the four chemistry students who attended a party the night before their final exam only to realise none of them were fit to drive home. So they stopped overnight, arrived back at class the next morning explaining to the professor that they were late for their exam because they had been studying at the library and got a flat tire on the way back, which made them late. Because they were straight-A students the professor accepted their explanation and said they could take the test the following day. He sat them at the four corners of the room and sat down to invigilate the exam. They all breathed a sigh of relief when they saw the first question, worth 5 marks out of the total 100, which was a very simple question about chemical reactions. Then they turned the page and saw "Question 2 (95 marks): Which tire?"
