I'm not entirely familiar with the inner workings of operational amplifiers. If I swapped the Vin+ and Vin- terminals, would that simply change the output polarity? (Not Vcc+ and Vcc-)

Thank you.

 

Basically, yes.
But if the op amp circuit has any negative feedback, it will change it to positive feedback and the circuit then will likely oscillate or latch up at one of the rails.

 

I'm not entirely familiar with the inner workings of operational amplifiers.

You don't need to be familiar with their inner workings, just their outer workings: what they are, how they behave in circuits, and how they are used. Pick up a good electronics textbook and start reading; our own online book is a good place to start.

If I swapped the Vin+ and Vin- terminals, would that simply change the output polarity? (Not Vcc+ and Vcc-)

It would completely screw up the operation of whatever circuit it is being used in.