I don't have a girlfriend nowadays, but if I had it, in most cases, I would prefer her not to dye her hair and to have haicuts just for keeping more or less the same length. I hate seen noticeable changes in a girl's hair length.
My ideal hair color and length in a girl is brunette to her butt but if she doesn't look this way the first time I meet her, she won't be more attractive for me by changing it. For example, if a had a girlfriend who I met with blond hair to her shoulders, she would become less attractive for me if she grew it to her butt or she dyed her hair brunette, because the attractiveness of a brunette girl with her hair to her butt has a very important psychological component for me: her pride about her natural color and always having so long hair. Of course, I would find it a breakdown if she got a shorter haircut or dyed her hair.
There some few cases that I prefer her to dye her hair: - She has natural grey hair, or her natural color doesn't look good. - The dye-stuff she is using is not permanent and it doesn't damage her hair. - Her current hair color is not natural because he has dyed it before. The only reason I prefer girls not to dye their hair is the sorrow of losing the beauty of her natural hair color, but if I haven't seen it or it is not beautiful I will prefer her to often change to color in which she dye her hair (and try some fantasy colors) than dying it always to the same color.
In some cases I find it glamourous for her to dye her hair into many different colors, but I won't find glamourous if she has a noticeable change of her length. The only case I would prefer a girlfriend to cut her hair shorter is if it wasn't nice and healthy and I would never like a girlfriend to grow her hair longer.