Elements, Customizer, etc.

Are you referring to this one here?
https://en-ca.wordpress.org/plugins/cookie-law-info/

I believe this one is quite well used and shouldn't cause any issues like that.

If you are sure then just try another one as don't have a specific recommendation for this.

That's the one. With everything else running, no problem. When I activate the GDPR cookie plug-in, poof! The Customizer develops widget amnesia.

I'll experiment with another plug-in option.

Meanwhile, thanks, David and Leo, for helping me see this through.

No problem :)