For the Yale incident, it seems this was basically just some people being mean to a couple professors because of an email blast they sent out. One of the professors still works for Yale and the other quit a year later, so it doesn't seem that anybody was fired over it, just more spilled ink. The one who quit has since had a book on the NYT bestseller list so even voluntarily quitting doesn't seem to have really hurt her career.
In the Mozilla case, this was basically just some people saying they disagree with the CEO of their company about gay marriage, and he eventually resigned. Even if he was really forced out by the board or something and the "resignation" is a nicety for the public statement, this just seems like a "risk" of making millions of dollars being a tech CEO. If your employees are gonna quit over some political donation unless you resign, your choices are basically: 1) let them quit, 2) don't write the check, or 3) write the check and resign. He probably didn't know he was choosing 3 when he wrote the check but lots of things in business are like that, and he probably could have chosen 1 if he'd actually owned the company but apparently he didn't. Also, he is now some other flavor of tech CEO (Brave Software, which seems to be trying to market a browser while also running what is presumably a crypto scam?). Again, no real consequences.
If "cancel culture" is just what we call it now when rich, powerful people have mean things said to them then yeah, it hardly seems to matter at all.