Which is why I use an external thumb drive with portable software and save any personal files to the thumb drive. It may hit their network but nothing is stored on their computers. Which gives plausible deniability - and I do not think they can legally search the thumb drive.

Not that I'm paranoid about my current employer (extremely relaxed culture) but it is something I do out of habit.

They may have the right to search your thumb drive if they believe you are downloading company data that may help the competition or cost revenue.

They have the same right to search your thumb drive as they have to search your house, which is none.