Your Microsoft Store account is different from your Xbox account.

I'm Samy an independent advisor. Welcome to the Xbox community. How are you?

These steps can help you, give it a try.
Check for updates on Windows Update, update everything including optional/additional updates.
1. Logout from Xbox app and Microsoft Store app
2. Look for the Xbox app and Microsoft Store app in the Windows menu, right-click, click app settings and then click terminate, restore and reset.
3. Clear the store cache type ''wsreset'' in the Windows bar, run as admin, and wait for the screen to close and open the store automatically.
4. Open the Microsoft Store app, click on the 3 dots in the upper right corner>downloads updates>get updates and update everything.
5. Restart your PC, log into the Microsoft Store and Xbox app and see if this solves the problem.

I am still having this issue as of July 2021: rapidly flashing login modal appearing and disappearing, the error message "Your Microsoft Store account is different from your Xbox account" appearing on every load of the Xbox app.

Launching the Xbox Console Companion (XCC) and minimizing it fixes the issue with the Xbox app. Meanwhile, the XCC app is aggressively messaging that it is EOL and we should be using the Xbox app. And yet, they seem inextricably linked. So which is it, Microsoft?

I am experiencing the exact same issue. Did you have any success resolving this issue?

Yes, any time I click on something while in the app, a pop-up will happen and quickly close a number of times in a row. It seems like the popup happens whenever it is loading something in the app? Not sure.

I had this issue after changing the email address for my Microsoft account. I could get into everything else, for some reason, but not Minecraft.

Opening the Xbox Console Companion app is the only thing that fixed it.