With the possibility of offending someone with the wrong comment, professors are now in fear of teaching and research on difficult ideas or complex historical periods because they could offend students and cause professors to lose their jobs. This is the most insidious form of restrictions on academic freedoms because the offenses are often subjective and decided by the "offended" party's feelings on the matter.
I do think that some professors feel constraints on their academic freedom; especially professors of science. The reason for this is because they are afraid of being laughed out of their profession and dismissed from their field as a quack. Or they're afraid of losing funding for specific projects they want to do.
Academic professors hold a wide variety of strongly supported opinions and beliefs. Surely some of them feel their freedom to voice these beliefs is under threat or constraint. This is not to say they are always correct in this opinion. That is another question. But certainly some do feel this way. This is not a debate question; it can be answered by simply looking at survey results.
I know in my experience with college I had some professors that felt they were constrained, but I feel like it was more a self imposed constraint than anything else. My economics teacher seemed to hate the class I was in, not the people, but the subject matter. I also had many teachers that were obviously free to do as they pleased and they did just that. Some of the best teachers I've ever had.
No, a professor is able to do what ever that they want to while they are teaching, and they are able to plan out there schedule in any way that they may seem fit. They do not have any constraints on them at all and are pretty much the boss.
I believe that professors do not feel constrained on their academic freedom. Unlike high school and middle school teachers, professors do not have to abide by strict state and national tests. This gives them the liberties to teach the subjects to their own liking. This is why professors do not feel constrained on their academic freedom.