I think it's less "ignoring sirens" and more "communicating about emergency alerts". Even if the siren legitimately went off during clear skies, people would be

I think it's less "ignoring sirens" and more "communicating about emergency alerts". Even if the siren legitimately went off during clear skies, people would be confused and you'd want a way to communicate why the sirens are going off. In most places around the US, they use the Emergency Alert System for that, pushing the message to TVs, radios, and cell phones. Already the EAS is set up with a protocol to let you know it's safe to ignore this alert, they test the alerts and say "this is only a test". And they already set off sirens that they expect you to ignore, in my area it's every Friday at noon.