Well, if you have an issue with people knowing you use Plex at all, then... tough luck, because I hate to tell you this, but a media server needs a client and it's a vanishingly small group of people that will use either Plex or Jellyfin clients and not let Apple, Google, LG, Samsung or whatever other device is running the client software that this is happening.
I give zero craps about whether Google knows I or anybody else uses Plex via their login because they already know this form the Google Play Store, along with the manufacturer of every TV we collectively own.
And for the record I do not live in the US and the way their absolutely idiotic copyright loopholes apply here is very much in question. It doesn't get tested in court much because the times it has been it didn't go particularly great for copyright holders. Private copying owned media is a right regulated by law here and I will continue to do so. If a corporation wants to deliberate with our local courts whether my owning a drive that happens to not be super picky about on-disc DRM I don't have anything particularly intense going on this week.
Ironically, in our own dumb legal implementation we are allowed to back up movies but there is a carved exception for software, so making a copy of a game you own is a bigger deal. Go figure.