Just swallow your principles and buy the ring. It's a few thousand dollars amortised over the length of the marrage. Over seven years it's like $40 a month which for a lot of HN is pocket change.
She can point to a bunch of stuff that you buy which has inflated price that you rationalise away as useful spending -- coffee from a coffee shop is a scam yet people don't think twice about it.
Edit: a word
To be honest, so is not being willing to buy a diamond for your partner that wants it, but that's the point, find another person who agrees with your expectations of them.
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.)
I agree, compromise is incredibly important and it's all about finding someone whose core principles are the same as yours. For me, the thought of having a partner who would argue and resent me over me not buying an expensive diamond ring would suggest a clash in core principles. But I completely appreciate that that's my own view of it.
I may change my mind to make her happy. She may change her mind because our financial situation has changed (mortgage). We may decide not to get married at all.
I don't consider this a core principle. Our views on the important stuff are very much aligned for the most part.
Coffee from a coffee shop isn't a scam because I'm paying for the accessibility, not the item itself.