If you're logged into your Google account when watching Youtube, it doesn't matter what browser you use - the activity would still register with Google.   Keep in mind the tradeoff is that FreeTube won't have your subscriptions and watching history - but that's the idea - you're breaking the link between your identity and what you're watching.

And you can get around this by exporting your subscriptions from Youtube and importing them into Freetube:
https://docs.freetubeapp.io/usage/importing-subscriptions/ 

 Oh wow, that is incredibly helpful. Thank you, sir!