I wouldn't resist solely on principle, if I find her idea interesting I might try it. However, if I don't like what she suggests she can accept that or GTFO. Ultimately I have the last say about my style, I won't lose my spine over a woman.
One could argue that hair style is unimportant enough to be worth less than pvssy. In that single case it might be true, but that's a narrow view of it. In the wider perspective you have forsaken a piece of your self-respect, a piece of your power over yourself. If you allow small things to pass it will add up and the sum is not worth the woman. Many pieces make up a considerable chunk, it would slowly eat away at who you are until you're in her possession. Then you'd get dumped for being spineless and since you have given away who you are you end up helpless in the face of reality.
Be extremely careful about pleasing others will about you. Every little thing seem harmless, but combined it can destroy you. I believe many guys here started giving in for small things that eventually developed into a very bitter experience.
No matter how small, stand your ground. If they try persuading you by minimizing the significance of the change, then flip the script and say "if it's so insignificant, you can surely accept that".