Is it rude to call a professor by their last name with no prefix in a non-academic setting? I always address my professors as "Professor [Last Name]" in an academic setting. However, in an non-academic setting such as running into them out and about, would it be considered rude to say "Hi [Last Name]!" to greet them? 

Would it be better to address them by their first name even if you have never used it before, or always prefix their last name with Professor?
I wouldn’t find it rude, but I would find it weird.  I can’t think of any situation where you wouldn’t be better off using a first name instead of a last name without a title.  If you’re going to be formal do it right, and if you’re going to be informal use first name.  We’re not on a football team or in the military.

(It’s of course totally fine and normal students talking to each other without the professor present, to just use last name and no title.)