Does inserting and immediately removing a node change a red-black tree?
It's not obvious that there is a "correct" answer to this question, as there are multiple insertion/deletion algorithms for red-black trees. Tarjan explicitly explains this in his book Data Structures and Network Algorithms, where he demonstrates (in section 4.2) update algorithms that require $O(1)$ rotations and references algorithms that require $\Omega(\lg n)$ rotations.

This is also mentioned in Hize's "A Simple Implementation Technique for
Priority Search Queues" and Driscoll et al.'s "Making Data Structures Persistent"