In my mind, the very worst (to them) is that if someone of one of those groups holds a position of any kind, they will always have the sword of "Affirmative Action Hire" hanging over their head either justifiably or unjustifiably.
When you see disaster occur to a place like Los Angeles due to extremely poor mismanagement or malmanagement and you find that the three most important positions bearing on the disaster are all lesbians, hired by people whose goal was not to manage the threat of fire, but to have more "representation" in positions of authority such as these three:
Then it isn't homophobia, racism, or sexism that causes people to think that people were hired not primarily on their suitability, aptitude, or competence at a given job, but for the various checkboxes that were checked in the hiring process.
If people are being chosen to perform a task that they fail at, and they are all chosen on the basis of something other than competency (such as skin color, gender, sexual preference, or, in the case of the doctored image above, moles on the right side of their faces) then normal, sensible, thinking people are going to rightly conclude that they were all chosen because they had moles on the right side of their face rather than their ability to manage the threat of fire.
And that damage that does to women who are good at their jobs who make occasional mistakes (as we all do) or blacks who occasionally have bad outcomes at tasks (as happens to all of us) or lesbians who make poor choices at managing the threat of fire (as administrators in the firefighting field sometimes do) is unfairly heaped on competent people who make mistakes as well as rightly heaped on the three female lesbians above.