1. ) In your line of work, having a "roommate" who is being watched so closely by the police sounds highly problematic for a variety of reasons.
2.) Rights, either yours or theirs, has nothing to do with it. It's what they can get away with.
3.) I would do as they say and remove the pix
Not sure what your roommate did to be under that much scrutiny but underage sex perhaps. Capital murder but he was young. They are usually lifers to checking in with LE. Perhaps you need to do a search of his records yourself to see what he did. Having a son in the house would certainly be a priority. Look on the sexual offender registry for your address. He would obviously be listed if that's the case.
If you go for a job interview they can and will ask for your face book info. In some cases can or will ask for your passcode to see if things are hidden. Do they have a right? By law they can refuse you employment and even fire you over what you have posted anywhere on the internet. Government employees have been fired for a momentary lapse of poor judgement making some stupid political remarks or not so nice pictures.
Kisses Haley
First, you have no legal case against police. Unless sealed by the courts your rap sheet is public record, and anyone can have access to it.
You haven't told us what convictions either of your records contain, but there may be a condition of his probation that he is prohibited from certain associations. They may have been warning him that he was in legal jeopardy of a prohibited association being discovered. You may think his record is BS, but the courts do not.
No one ordered you to do anything. Sounds like someone was warning him or you, or both that publicly displaying your association puts one or both of you in legal jeopardy of some sort. They cannot force you to take down pictures, they can use those pictures as evidence of a violation of probation.
You have no expectation of privacy from something posted on a public forum such as FB. That's why it has all those legal warnings about who can or cannot see things.
They are not stalking you, they are observing the actions of two people with criminal records, at least one of whom is still under court supervision.
Sounds like your friends PO was trying to do him a solid, and if you leave his pictures up you may be putting up his pictures in an orange jump suit. If your FB is only for family, do your friend a favor (or maybe yourself) e-mail them the pictures and get them out of the public record.