Let's ask a different question. Should teachers/educators be on social media? Yes. No question. If we want to connect with students and meet students where they are, social media is the way to go. Educational research tells us that we need to be relevant to engage students effectively. It also tells us that if we can extend our time spent on learning and our curriculum, then achievement goes up. Now put those two together. If we engage students with relevant questions/topics and use a medium that they are using outside of school for socializing, we are likely to extend school related discussions that promote learning, inquiry and authentic application of concepts in the real world. Many have unpacked this much more than I am here. This is only 1 aspect of leveraging social media to benefit learning.
I think the "friends" on Facebook is a bit more complex. Some people advocate 2 accounts...1 professional and 1 personal. I think you have to think about how you use social media. I have some accounts that are personal and my friends/links reflect that. I have other accounts that are solely professional. Based on our roles, this can be easier for some than others. For me, Facebook is personal. There is nothing on there I'm ashamed of. Actually, I don't post much. Rather, I use it to keep up with friends across the world. I also don't have a class of students that I work directly with right now with my given role. Twitter is my professional account. Don't get me wrong. The personal nature of who you are bleeds over into the professional as well it should. It is reasonable to keep the two separate. Bottom line, if you are posting things that students should not see or might be better left to their imagination, don't friend them on Facebook.
No matter what medium you use for social media and connections, your life is more transparent than it has ever been. We know more about each other. Modeling and making good choices is paramount. So is self-control. You can't post confidential or "soon to be public" info before it actually is public. Many people have had some heavy consequences for mistakes in this area and it deserves due caution. All said, social media is a place to extend learning and leverage for the good of both student learning and professional learning. Don't be scared. Jump in but do so with some thought and foresight.