I'm sure this varies by location, but in many jurisdictions it's legal to use the other gender's restroom, particularly in cases of great urgency. Occasionally this has surprised previous occupants - although at least anecdotally there's an interesting disparity. Women seem to worry about it more and men seem to be more often surprised by the actual event. I'm not sure if anyone has hard numbers on that.

Not relevant to the sex offender question except to note that there are a lot more normal people with momentary plumbing needs.