The quoting verb is omitted. It’s similar to how we say “the law that (says that) you aren’t allowed to steal” where you can omit the “says that” part.
To me it’s not so confusing, but I did just wake up (so maybe I’m not thinking straight)
下着の色を決める is the core of the sentence
白と marks what they decided the color to be
規則で means “as a rule” or “by rule”
This と is the same kind of と as in となる. We don’t have to get into how になる and となる are different here, but (noun)を(noun)に決める and (noun)を(noun)と決める is a similar set.