What am I going to do, quit over using an app?

Why quit?

Ask them for help installing the app.

Then bring in an early-2000s flip phone with your SIM already in it, so you can prove that you are using it.

An employer cannot demand that you buy your own work tools unless it is written into the employment contract (auto mechanics, etc.). Provide them with a phone that they themselves cannot install the app on. Any early-2000s feature phone will not have an operating system with app functionality. An older but still smartphone-like BlackBerry running BBOS10 will also work in this regard, especially if you have uninstalled the Amazon App Store.

Even an Android phone whose newest possible version of Android pre-dates the oldest version that this app will install on can also work. For example, any Android phone which cannot be upgraded past Android 7 would be perfect with respect to MS Authenticator, as the current version will only install on Android 8 or newer. If you bring in a phone that has no ability to have Android 8 or later installed, your place of work will either have to exempt you or provide you with a work phone for that app.

You have solutions to keep work apps off of your personal devices, and few employers will have the legal ability to force you to buy a modern phone just for an app of their choosing. Moreover, it is your right to not have to suffer unreasonable employer demands just to have a job. That’s why worker protections exist in places where conservatives haven’t eviscerated those protections.

Act like you are a smartphone-phobe, and let them figure things out.