If it were say, an African American student who put up some sort of incendiary statement of some kind against another group of people, I think I’d be inclined, as either an educator or administrator, to take the student aside for a serious discission about his/her future, and how an action of that sort could impact it going forward. With accompanying disciplary action. What I would NOT do is inform potential colleges (unless I perceived the student to be an actual threat of some sort), because that’s only going to get a student blackballed.
High school students do dumb things without a lot of forethought. Unless a clear pattern has been established I think there’s more benefit to trying to give the student some insight rather than trying to ruin the student’s college chances.
Whether it be a swastika, gang symbol, or other sort of slur.