I'd speak to management and voice your concerns regarding the app, and ask if there is another method available for entry. If not, I'd cancel my membership and look for another gym that respects my privacy.
It's not implemented yet, but tubearchivist https://github.com/tubearchivist/tubearchivist has a podcast mode on their roadmap which I've been keeping an eye on.
I'd speak to management and voice your concerns regarding the app, and ask if there is another method available for entry. If not, I'd cancel my membership and look for another gym that respects my privacy.