hemlockiv I assume it's this one: https://play.google.com/store/apps/details?id=com.adobe.premiererush.videoeditor
I installed it in a profile without Google Play services and it refused to start without it. In a profile with Google Play services not signed in to a Google account it just redirected me to Play Store. When I'm signed in to the Play Store I can then sign in with my Adobe account.
Unfortunately nothing you can do about this when the app refuses to work without it, short of contacting Adobe and asking them to remove the requirement.
You could of course create a profile just for this app, install Sandboxed Google Play and create a Google account just for that profile. Although I'm not sure if the app is able to see the account name / email address of your Google account (I don't know the technicalities behind that).
hemlockiv I tried side loading a much older version of Rush from apkmirror, and while that one doesn't enforce the same Playstore login, iit still throws an error when I try to sign in with Adobe ID.
Apps are able to send the version number to the server that it contacts, and the server can refuse to sign you in if you're on a certain version or an older version than version X, or whatever they decide to check against. This could be for any arbitrary reason, such as the developers wanting to protect users against versions vulnerable to a security flaw. Mind you, both memory tagging and hardened_malloc detects memory safety issues in this app… Or perhaps they just don't want user complaints caused by them using an old version with lots of bugs.