I am a first year PhD student in Europe, I started in November. My supervisor has recently take a liking into posting on social media and communication-related issues (style, words, hours etc), even for subjects that are not strictly related to our laboratory academic activities. Since he was also my supervisor for my master thesis, I know for a fact that he discovered Altmetrics only a year ago or so.
Problem: today he basically demanded that whenever he posts on social media something that's related to the lab activities, it is mandatory that all members have to like and share on their personal account the post or whatever that will be.
There are other issues with him, but in this case I think that this is a violation of personal space: I should decide what to post or like with my personal social media account, not my supervisor or future employers.
Question: could he even think of making this kind of demands?
Edit: I know that for someone could sound like a rhetorical question (to me, it sure does), but I wanted to hear others' opinion on the subject.
Update: I managed to apply and then win a PhD position abroad in a better university, with a more stimulating working environment and a more professional group. It was fair on my end to tell my supervisor that I was about to sign a contract and quit the current PhD program: it was fun that in this situation, while I was explaining that I was planning on leaving, my behavior was labeled by him as "unethical". Furthermore, if we were to collaborate in the future for any kind of reason/project, I would be stigmatized, as in labeled as "unreliable" for the decision of quitting/leaving (a low-key professional threat basically).