I'd suggest that the Milgram experiments illustrate this beautifully, even if they're dated, and I often wonder if we'd get the same results today (not that the second one would ever get past an ethics panel, now).
First, there's the one where he walks onto a subway train and just goes up to random people and asks, "May I take your seat?" and they just get up and let him sit down.
Then there was the more well-known one, which I'll detail for anyone who doesn't know. In this experiment, people believed they were "punishing" another participant (who was really an actor) in the experiment by pressing a button that apparently (but not really) gave an actor an electric shock when they gave a wrong answer to something. When encouraged by the "researcher", the participant with the button pressed it up to 400V, even when the actor screamed, and even after the actor stopped responding.
This has often been used to explain just how Nazis were en-masse participants in war crimes, but it can also explain low-level "following" of very dubious "leaders" such as "thought leaders" and "influencers" (and MLM hunbots). There are so many of these on places like TikTok and Twitter who are peddling the trans narrative.
People's deference to authority and belief in authority are powerful and dangerous things. This is what organisations like Stonewall and Mermaids are exploiting. They put themselves in a position of authority, they get lots of "big names" behind them (like the Civil Service... it doesn't get much more authoritative than that) and then they push their agenda from a platform of power. People might not recognise them, but they'll recognise who they are associated with and that authority then extends to Stonewall/Mermaids, giving them a false aura of legitimacy.
As women have pushed back and gained legitimacy with their own associations with "authority figures" such as JKR, they have gained ground. I think it helps that for a lot of people, the GC movement sense-checks/confirms what they already thought, and unearths those little niggles they had in the back of their mind about the official-sounding false narrative that keeps being pushed on them.