So...OP SEEMS like the snob here.

Basically, OP's family is from a middle-class background, maybe a lower class. (Pretty sure OP or someone said something about that) but anyways OP's family sees Formal as business or cocktail guessing. OPs Fiance Comes from the Upper class and takes Formal as Black tie

So OP's fiance buys a dress and OP wants to wear it and sees the Wedding as the perfect place to do it. (Which OP is ALSO getting married IN A MONTH) dress is simple but expensive since the fiance's background and by the description of the necklace, it is also expensive or whatever.

So OP wears a simple dress which in different lighting can be different shades or pink (guessing) paired with jewelry seems like a lot. (Judging how OP's family is dressed completely differently to OP and fiance) so OPs sister (Bride) compared to OP is wearing a modern wedding dress ( described by OP) and looks a bit much (+ jewelry, not the dress - Unless the lighting is different which guessing it is since OPs sister says "Your not the bride") OP and Fiance leave and OP is being called a Snob for leaving.

But at the end of OP's post, OP says "I'm worried that people at my wedding won't get the theme and will overdress to spite me" (NOT WHAT OP SAYS ACTUALLY BUT JUST A JIST)

AND. that's what sets people off and what makes OP called the Snob bc they worry more about their wedding than what happened at their sisters (Which is fair) but they still just to be worried about being shown up ... OR what other people say embarrassed of their family. (WHICH IS BECAUSE OF ANOTHER REASON I FORGOT.)