Is it possible to sort questions by active comments, so the questions with the most recent comments appear at the top?
No, it is not.
Of course, you could make your own userscript for this but there isn't a question filter for this currently. Anyways, with high-traffic sites like Stack Overflow and Super User, the list would update itself almost instantly and be a bothersome to users currently using a comment type question filter.
Comments are considered as less important than questions.
Comments are often used to ask for clarification on, suggest corrections to and provide meta-information about posts.
So, Visitors post comments on the questions mostly for the improvement of questions. In order for a question to be focused (i.e active), it needs to be revised. Otherwise I don't think there is any purpose of filtering such questions (which are not actually active) based on comments!
Currently there no such feature to filter those questions, However If you want, you can write user-script for that as said in this answer.