I’d say drop it and accept your wife how she likes to be. It’s not “nothing” but it’s just outer appearance and ultimately she has to walk around with her body and be comfortable with her looks.
You two should talk. Respect each other and find something that works for the both of you. Focus on how you and her feel and what your wants and needs are. In doubt she gets to decide on her own haircut. But try to find out why it’s bothering you and her so much.
Edit: And I’d agree on the couples therapy someone mentioned. This isn’t a healthy situation to be in. You probably need to put in some effort if you want to keep her. Learn how to accept each other and grow past this. I’m not saying you’re at fault or the one needing to change. But the underlying issue could drive you apart if it keeps growing.