iPad won't let me update apps after update to iOS 14 Since updating iPads to iOS 14 I am not able to update apps. After hitting update I am asked for password which I do fill correctly. After about ten seconds the password dialogue appears again, and again, and again.
I do remember on both iPads Apple tried to force me into two factor authentication which I absolutely do not want. I have clicked on Later as there was no other option for opting out.
What can I do to be able to update the apps? Of course apart of setting up two factor authentication?
As of June 17, 2020 you can not turn off two-factor authentication and you can not use some features without enabling it. It was optional, highly encouraged and opt-in on iOS 12 and iOS 13.

https://support.apple.com/en-us/HT204915


Can I turn off two-factor authentication after I’ve turned it on?
If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information. If you recently updated your account, you can unenroll within two weeks of enrollment. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require higher security.

I have not tested the unenrollment in the two week grace period but have no reason to believe it won’t work as described. The services Apple ties to two-factor (which is easily confused with the previous two-step process)  have been changing outside the iOS major release cycle
The only thing that’s changed with iOS 14 is Apple removed the opt-in UI since the services themselves are now forcing the upgrade in security.
You still want to closely manage all the security at this page whenever a device gives you a hassle or unexpected challenge. (This much hasn’t changed in many years)

https://appleid.apple.com/account/manage

Once you review your current settings above and make the security page happy, you may have to choose between this model requiring a second factor past your password and managing the prompts, trying it and declining the features or just letting the features that mandate this fail and go unused.  It appears you could also keep using older software with two-step or relying on the security questions and just a password for existing AppleID.