Not really. In both cases, compulsion is the problem. Neither side has the right to compel anyone to do anything, but they operate on the premise that they do, usually characterized by indignant self-rightiousness. The irrational extremists of both sides, the ones screaming the loudest, naturally, seek to enforce their version of "how things should be" on to other people, regardless if their objections are rational or not, while also constantly changing the rules or shifting goal posts, which keeps us forever locked in a state of not knowing if we are breaking them. It's mind-numbing to a degree that apathy starts to seem like a perfectly valid option. It's also a tactic historically used by totalitarianism.

They are two sides of the same monster, like Jekyll & Hyde.

Surely one can find ways to fight the irrational, inconsequential leftists (which there are many) without bullying institutions by cutting their funding, or kidnapping people in broad daylight in the street?

Civilized western countries do it all the time.