I think there are some terms which should be defined in order to understand the question:
By course do you mean a semester-long sequence of lectures and exams in one subject? This is the US usage, while in other places module is used. In those places course means what in the US is called a degree program: the set of courses/modules taken to complete the degree.
Are you asked to "like" a Facebook page or "join" a Facebook group? Both have been used interchangeably in this discussion but they are not the same. A Facebook page is used by an organization for self-promotion and broadcasting information. It's mainly a one-way tool, though likers can comment and (sometimes, depending on settings) post. A Facebook group can be official or unofficial but is used for multi-way communication among its members.
If a course-as-in-degree-program is asking you to like their Facebook page, it's probably just to open up another line of communication to you. For instance, they might use it to broadcast that the university is closed for bad weather, and you can get that information before checking your email. You can do this without using Facebook for anything else; you don't have to interact with the other fans of the page. I believe fans aren't privy to who is and isn't a fellow fan.
If a course-as-in-degree-program is asking you to join a Facebook group, it might be more for discussion as for a group, but would still be non-academic. Perhaps they want to collect opinions about services. Group members are able to see the list of group members, so you would be known. But you don't have to be (Facebook) friends with the fellow group members, so you can interact with the group and keep the other members at arm's length.
If a course-as-in-module is asking you to like their Facebook page, it's going to be academic but still mainly broadcast. I've done this in my large lecture courses to announce when slides are posted or reminders about due dates. These are useful to get extra communication to the students, but they should not be used to publish anything that's not also on a university website. If you find that there is original course material published on Facebook, you might want to raise concern.
If a course-as-in-module is asking you to join a Facebook group, it's likely that it's for academic discussion. This can be beneficial as others have pointed out. And the interface is familiar to most students so the content can be quite rich. But if the Facebook discussion is to be graded that's the most problematic combination. Joining Facebook requires individuals to sacrifice a considerable amount of privacy, and I think it's not fair for university officials to explicitly require that consent to participate in instruction. If you have a problem with joining Facebook and the instructor wants you do so for a grade, you should definitely be concerned.