Can't think, offhand, of situations exactly fitting your suggestion. Apart from the usual stuff of football fans hurling racist abuse at players from the "enemy" team, but sadly this is normal for the idiotic majority of football fans. But I will, as you put it, "go for it" (listed in the ghastly expressions thread) anyway.
One aspect concerns trans-genders. In many sports men who have become women do, or would like to, compete as women. But this gives them an unfair advantage over women who have always been women. Which is demonstrated by the fact that there are no instances, as far as I know, of women who have become men who want to compete against men who have always been men, since they would be at a disadvantage. So, OK that you can choose your sex/gender, but what happens when this is unfair from the sports point of view?