This is basically the problem, as I see it.
On one hand, keep the speaker. The potential downside: social media outrage that may escalate and get covered on MSM if it gets big enough. You and your dept / uni get a lot of bad press or if things go really sideways, your job could be on the line.
The potential upside of this decision? People go to a talk and consider some issues, but it’s not like you (the committee / administrator / dean etc) get any real tangible incentive from this outcome. You basically just did your job, if you’re lucky, everyone just moves on.
On the other hand, cancel the speaker. The upside: MSM will congratulate you or ignore it, but regardless, you’ll be seen as making the “right” decision by most people you interact with. Some free speech types (a dying breed it seems) might get upset but they don’t seem to have much power over the general public’s perception or decisions about firing made by the university.
So the decision is obvious and it’s the one that gets made time and time again. And it’s the way the Twitter mobs continue to hold sway, especially because so much of the MSM lives on Twitter.
A similar rubric occurs in a large corporation by the C suite. Once the mob forms, there is everything to lose and almost nothing to lose by taking a stand on an issue seen as unwoke. If this is to change, incentives need to change, mainly creating disincentives for cowardly execs / deans and incentives for those who make principled and/or courageous stands.
(None of this is a carte blanche endorsement against activism, it’s just to say that there are reasons that no one stands up against Twitter mobs and we may want to explore ways to change this dynamic unless we desire a future ruled by mobs)