No pressure from my institution, which is very supportive of academic freedom. But I'm lucky in being where I am. Other professors are not so lucky, and I stand in solidarity with them.
In general , people in the political and cultural Right place direct and indirect pressures on teachers and professors to limit discussion to certain dogmatic truths. My institution doesn't cave to that pressure, but others do. Right now, the U.S. Right is wants professors like me to not discuss racism and sexism in particular. It's not just the abuse I receive on social media, it is an organized social campaign.
David Starkey is a very well-known TV presenter in the UK, so when he spreads falsehoods like this, he reaches many people.