Is it acceptable to extend deadlines for coursework delayed due to student activism?

Much would depend on the concrete situation. But, by default, I would think that activism is part of student's life that the student needs to learn to manage themselves; if they do not have the resources or ability to manage their activism effectively so as not to have them interfere with their studies, then, largely, I would consider this to be their responsibility. One would probably not see any concessions given for extracurricular sports/music activity, and the question is why political activism should be exempt.

Some may argue that political activism is important as a part of society and therefore of a higher rank than, say, sports or music, but how this is evaluated would probably depend on whose side of the activism one sees oneself.

That being said, times which are more tolerant of studies as an opportunity for character development would probably give more leeway to activism, while times (such as ours) where studies would be considered more a means to an end (development of employment skills) would probably be less tolerant. I would see the former as an ideal of times past, but the latter as the reality today.

Lots of good and lengthy answers here: put concisely the answer is a resounding no.

A huge benefit of choosing to do something extracurricular in college is learning the consequences of failing to balance responsibilities. By giving extensions to a student that chooses to spend time doing something outside of coursework, you fail to help them find this balance.

I try to always spell things out like this in my syllabus, and I would hope others do, too. For me, I would excuse a small number of minor things, so long as warning is given in advance, but it wouldn't be a valid excuse on a test or especially major assignment.

I don't have a specific clause for activism, nor have I gotten excuses from that activity, but I've given leeway for other legitimate student activities (sports, coding camps, etc.) and this would be no different.

Other teachers in my department would feel differently, not giving excuses for anything but medical or religious leave, but the point is that this is spelled out in advance, which is the only way it ever should be. Students should understand the consequences of their choices and be bound by them.