Is it possible for my code to exercise a second REST endpoint while another one is in progress?
If it is, then I have to ensure my generic REST handling code on the client is also re-entrant.
From another thread, yes. Your code should be 100% thread-safe.
About reentrancy within the same thread, it's rare, but I'd recommend that all your REST endpoints are implemented to be thread-safe and reentrant, this will make your server more reliable.