One persons rights ends, where another persons rights begins.
Rights apply to people, not corporations (no matter what the dumb ass supreme dunsel court says). But even if rights applies to corporations, then their individual rights of free speech does not trump your own.
Their attempts to even look at a persons faceboo page is used as a way to manipulate applicants and employees into saying what the employer likes, or they are retaliated against, and that goes too far.
Now, asking for the actual login, goes WAY too far; next they will be asking for the password to your bank account. You need to make a stand and tell them no. If you don't, then you are only contributing to the problem.
On the other hand, turn about is fair play. You can "leak" their passwords if you can find the access to it, and you can go to the facebook and get lots of information on lots of employees officers, and owners. and do whatever you like with it.
Turn about is fair play. They impact your job and ability to make money, so you impact their business, and ability to make money.