Reps has no sign-up, no login and no account of any kind. It has no ads, no trackers, no analytics and no third-party SDKs. The App Store privacy label reads Data Not Collected, and the label has nothing else on it.
The important part is why. There is no BSR LABS server. Nothing you write in Reps is transmitted anywhere, because there is nowhere for it to go. This is a property of how the app is built rather than a promise about how anyone behaves.
Most privacy policies describe what a company promises to do with your data. The more useful question is whether they have it at all.
Syncing runs through your own iCloud account, in the app's iCloud Documents container. Apple holds that file the way it holds your other iCloud documents, under your Apple Account and Apple's terms. Nobody at BSR LABS is anywhere in that path.
Clinical students write cards about real cases. Law students write cards about live matters. Anyone in a regulated field ends up with study material that has more in it than they intended, and the safest place for that is a device they control.
The same logic applies to anyone who simply does not want their study habits, their weak subjects and their exam dates held in someone else's database.
Because nothing needs to check in with a server, Reps works with no connection at all. Airplane mode included.
No. There is nothing to sign up for.
Your cards are files in your own iCloud account on your own devices. They keep working.
Your data sits inside your own iCloud account under Apple's protections. It never travels anywhere else to be protected or not protected.
Yes. You lose syncing between devices; the app itself works normally.