I would get the cut and if the wedding is fairly close to my birthday, I'd probably wait to color it. But I'd also talk to my sister and discuss with her the negative aspects of what she said to you.
1) She doesn't get to dictate what you do with your hair just because it is her wedding. She can either take you for a bridesmaid as you are or leave you out. You holding off on the color is a courtesy you are extending to her, and in no way something she is entitled to.
2) It was hurtful for her to imply that your appearance is more important to her in having you stand up for her than the relationship the two of you share.
The reasons why I'm thinking you should extend the courtesy - well it seems like you've already had tension over other aspects of the wedding planning. Even if it isn't true, it would be bad if people got the impression that you were being difficult, something this particular instance is likely to encourage because people can be really dismissive about conflicts over hair and appearance "Oh it's just hair! Let her have her day!" or "Purple? You want wear purple hair to your sister's wedding?" or "Why are you trying to steal attention away from your sister?"
Basically, this is one of those situations where you may very well be right in the abstract, but you'll likely be the one to take a hit in reality. In this situation, I'd rather know I'm right in my head, but let it go and have others see me as gracious, rather than dig in my heels and have others think I'm just causing trouble.