How can I stop the App Store asking for a password in OSX?
Solution 1:
As of macOS Big Sur 11.1, there's a setting in "System Preferences" » "Apple ID" » "Media & Purchases". Change "Free Downloads" from "Require Password" to "Never Require".
Solution 2:
No, in the current version and previous versions it will require the password to update, however I believe the version to be released in the fall removes this requirement.
You can however fix this by enabling automatic update.
Solution 3:
I know this answer comes a bit late but, in my case, it happens all time because applications were downloaded using different iCloud accounts.
The App Store doesn't show any more detailed information about it, but, in my case, the Apple ID shown when asking the password (grayed out in the textbox) seems to be the one it is requiring. I entered the password of that account, even if they were not the usual App Store account, and it worked perfectly.
Hope this clue can help you.
Solution 4:
There's always this setting in Settings > App Store
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