As you said (essentially), 'they did it because the media told them to do it because [insert false reason here]'.

If that's true (and it is), then they follow whatever the media says -- and the biggest message the media has for them is 'we must fight global warming [if we don't do X, Y, and Z]'.

So, in the majority of cases (for 'that' kind of parent), I don't think the button would be pressed. I think 'those' types of parents would 'proudly wear their unpressed button around their necks' to show how obedient they are.

Then again, (in the speech) he wasn't talking about 'woke parents in first-world countries'...