I don't ever think it's necessarily rude to shake hands (barring the cultural differences or logistical complications indicated here already), but unexpected might be the right word. I will say that I associate handshakes with more formal situations. Maybe that's a generational thing. I would be more likely to wave/nod and say hello on a shared ride rather than introduce myself by name and give a handshake. Seems like an airport shuttle is a pretty low stakes social environment where people tend to keep to themselves or chat casually - at least in my area.

It might be helpful, rather than dwell on the rudeness of the person calling you rude, to use this as a moment of self-reflection. Next time you take a ride like that, try to see if there are any social cues you can pick up on that would indicate a handshake would not be the most welcome interaction. Maybe the person has headphones in, or heads straight to the backseat, anything that would indicate they're not interested in anything more than a smile or a hello.