We sometimes used to allow our child to dress in fancy things or fun things to go out in public, but made sure she understood "this is just for fun". Or she could wear the hat or Tail all of the time, "except to dance class". then I would "hold onto it till she was finished with dance".
Make some allowances, but explain there are just some times, we have to dress "normal"..
At our daughters dance classes at this age, no tutus were allowed for this exact reason.. It was pink tights and black leotard and pink shoes. All of them. They all looked exactly the same.
I think our daughter did not try to be like the others, but had her own preferences from an early age. Until kindergarten, she loved dresses and jumpers. Refused to wear pants. NO tennis shoes. She was fine with shorts and wore them under her dresses or wore "bloomers" and leggings.
In Kindergarten the school had rules about every child had to wear tennis shoes everyday. They all run track every day. They suggested shorts under all dresses and still leggings.
It was not till about 3rd grade, she decided she wanted to try on Jeans. Once she was in middle school it was jeans and tshirts.. She was famous for her tshirts. She even designed and printed on her tshirts. (Artist) NO DRESSES! Skirts.. were ok if she had to wear one.
This continued till she got to College.. Now she is better at dressing like a grown person, she had an internship this summer and only wore dresses.. My husband was over the moon. He loved seeing her dressed up. She seemed to really get into the shopping and dressing up.
Try to work with her on some types of choices. Also let her know her attitude makes a difference. Good attitude, positive out come.. Fits, are ALWAYS a no.