Is it acceptable to extend deadlines for coursework delayed due to student activism? This article from the Brown University Daily Herald describes a number of student activists who claim to have suffered due to excess levels of student activism. Some excerpts from the article are included:

“There are people breaking down, dropping out of classes and failing classes because of the activism work they are taking on,” said David, an undergraduate whose name has been changed to preserve anonymity. Throughout the year, he has worked to confront issues of racism and diversity on campus.

[...]

Sampedro worked alongside the group that presented the demands for the diversity and inclusion action plan’s revision. It was a Thursday, she recalled, and she had a research presentation that needed to be completed that week. “I remember emailing the professor and begging her to put things off another week,” she said. The professor denied her request.
“I hadn’t eaten. I hadn’t slept. I was exhausted, physically and emotionally,” she said. After hours of work to compile and present the demands, she forced herself to stay up to complete the project anyway.

[...] (emphasis mine)

Deans’ notes helped Gaines to complete academic work while staying involved in student activism.
In writing such notes, deans acknowledge the difficulties faced by a student on campus and demonstrate their support for the student’s requests, said Ashley Ferranti, assistant dean of student support services.
Though it is ultimately up to a faculty member to accept a dean’s note, Ferranti estimated that notes are accepted over 90 percent of the time. Students who take issue with the rejection of a note can discuss the incident with a dean, Ferranti added.

I was under the impression from my personal experience that extension of deadlines are generally only awarded for reasons such as personal illness or family issues such as divorce, death, or serious illness.
As professors, is it generally considered acceptable to provide deadline extensions or other accommodations to students who have fallen behind on their coursework due to their involvement with 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.