Another confirmation of this issue from me. I use both Astra and Gutenberg. After the recent Gutenberg update, the customizer stops working.
Suggesting anyone for using a backdated version wouldn’t be a wise opinion, but you can do it at your own risk. I’ve checked the immediate previous version (10.7.0), but the problem was not solved. The version before that (10.6.2 to be exact) doesn’t affect the customizer.
Versions 10.7.0 and 10.7.1 come with two different “PostCSS Plugins Preset” security patches. Using 10.6.2 could solve the customizer problem before they fix it.