well, one Child molester I knew was specifically forbidden to go to church (children there). A woman was forbidden from contact with her daughter (who had an outstanding warrant on her). Yes, the agents could search any/all property associated with the person at any time w/o permission w/o probable cause (I used to do room, purse, pocket etc searches all the time) and of course have to pee on demand (yes, did that,too. Can’t pay me enough anymore to do that one). Travel is restricted as well - for example, travel outside the state is rarely permitted, and in some cases, they cannot travel outside their county of origin, either w/o specific authorization. If they’re on tether, they must have prior permission before going anywhere (including stopping at a store on the way home), must be back at the specific time.
Seems to me that they (D o C/courts) have a tremendous amount of latitude when devising these terms and conditions. Where they live, who they can be with, what places they can go to, what they can/cannot have in their possession (computer for example), where they can work. What kind of jobs they can take (sometimes necessitating career changes while on supervision - for example a contractor may not be able to work at that field since they may move from job site to job site during the day - and some parole/probation conditions do not allow for that).
Certainly, they’re not allowed to be in possession of guns or be in a house where guns are stored.
They are required to give “true and complete” reports of their behavior, which can be considered to be a violation of the 5th adm. I’ve seen cases where they were not given the option of refusing medical treatment (one case we all had to get vaccinated against Hepititus, one tried to refuse, she was forced).