True, but... for a public institution that leans left to give in to pressure from the right is going to mean the right thinks they can push that institution around with pressure. It's to open the door to a lot more pressure.
Of course, the right way out of this dilemma is to, once it's brought to your attention, ignore the pressure but handle it like you should have handled it, and with public statements of status. "We are aware of the allegations. We have formed an independent committee to investigate. Until that investigation terminates, we have no further statement." And then a public statement when it has terminated. And so on. Then you're doing the right thing, but not responding to pressure.