I use a fairly aggressive DNS setup (a server added in the Gnome network settings), blocking Google domains and payment processors, which are embedded on the majority of the web. Is it trivial to launch a browser instance which would use the default DNS server (‘automatic’), when doing online shopping for instance?
I prefer avoiding any persistent settings – only apply the stock DNS settings when requested by the user (and obviously not system-wide!):
--default-dns chromium
I think you should run Pi-hole (on a Pi Zero or in a Docker container) with unbound as resolver to block any unwanted domain queries. And whenever you want to use google or online shopping you quickly disable Pi-hole (comes with timers, for example 15 minutes).
That way you are your own DNS service and should have full control.
You can override system DNS with these methods:
Firefox + DoH:
Preferences > General > Network Settings > Settings… > Enable DNS over HTTPS > Check > OK
Virtualization:
Installing virtual operating systems with GNOME Boxes :: Fedora Docs
And alternatively a new dedicated profile can be created in about:profiles and switched to when needed.