> Because most "woke" stuff is made up or blown out of proportion by people on the internet.

I think you are misinterpreting the issue. I'll explain why.

There are attention-seekers which were given access to platforms with unprecedented reach. Some of these types tap into outrage culture as their engagement mechanism. This creates a vicious cycle of outrage which feeds on outputting outrageous claims and taking the resulting outrage as input to further double down on outputting outrageous claims. You then end up with opposing outrage camps of whatever subject you can think of which exist to generate a larger volume of outrage than the opposing camp.

The problem is that the terminally-online types confuse this sort of discourse with reality, and the outrageous claims as representative of what happens in real life. That's how you end up with people outraged with outrageous claims that are so outrageous to the point they are unthinkable.