I couldn't imagine being happy in a relationship without learning to compromise. Only the most important things should be considered "core principles", questions of religion, child-rearing, maybe hot-button political issues, and other moral litmus tests.
Whether or not she gets the ring she wants is a silly gender identity fixation, pretty harmless in comparison. If its a core principal, then so is whether or not he's allowed play video games, or buy a motorcycle, and so on. (Btw, I'm not engaged, married, nor ever bought a ring.)