I think by now, most people who post online realize that a public profile is just that, and they run the risk that anyone, from their fifth grade teacher to their priest to the janitor at their office, could potentially see it.
It would not be rude for anyone to read online information. It's tantamount to a billboard on the side of a highway. This includes coworkers, be they subordinates, superiors, or equivalent in position.
Depending on whose it was, I would probably find it irresistible to read certain profiles.
But, in general, I probably wouldn't even bother, because most people are boring.
So, the tl;dr here is, not rude, and really imperative on the site user to decide what to put out there for any or all eyes to see.