Looks interesting -- however much of the app does not work if www.googletagmanager.com is blocked. Is that necessary to the functionality or just an oversight?
If a site doesn't work properly with GTM blocked, legitimate use case or not, personally I normally just move on. Unless I have a compelling reason to need that site, I won't make any attempt to work around it or change my blocker settings.
The only Google property I'm aware of that isn't routinely blocked by these kinds of tools now is Google Fonts, and I think some of them even block that by default now.