Possible solution for you.
I had this same issue and it drove me insane entering my password every... single... time I updated an app. I’m uncertain if you need both of these changed but this is what eventually fixed it for me.
First of all the standard thing to do looks a little different in iOS 14 (they hid it a bit) but go to settings, click Apple ID at the top, click media and purchases, then click on the little person at the very top of the pop up next to where it says account settings, now click password settings in the new pop up and make sure require password for free downloads is turned off. This alone did not solve the problem for me. Maybe it will for you but if not try the next step as well.
So here is where I think the issue is 😂... on to the 2nd random buried setting in iOS 14. This did solve it for me oddly enough. Now go to settings, click on Screen Time (yep), then click content & privacy restrictions, after that click iTunes & App Store purchases, now go down to Require Password and click Don’t Require. 😓 This fixed it for me after signing in again. I would say make sure your device is secure after changing this to avoid accidental purchases.
I’m unsure if you need to do the first settings change since I already tried that before the screen time hide and seek setting but I would assume so. I talked to apple support first and they went through the iOS 13 steps and obviously that won’t work because they hid the don’t require password button in a different spot and then with the updated security features (which I’m thankful for) hid a second setting (in a place we generally wouldn’t look) 😅😅.
Please let me know if this worked for you guys also. I’ll try to start a thread for the other people googling until their eyes bleed to make the password prompt stop. Thank Eric Root for responding to my desperate search for an answer phase and suggesting I post the solution I finally found.