Disable password after screen saver begins

So you're saying that the menu shown here is greyed out, right?

Then try the following: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

If you can not set "Require password after screen saver or display is turned off" to Never.

It is because the Mac's iPhone Mirroring App setting is preventing you from changing that setting.

To fix that, open the iPhone Mirroring App on your Mac, go to Settings and change the setting to "Ask every time"

Now then, you should be able to set "Require password after screensaver begins or display is off" to Never.

Do you use an iPhone?

Ref: Cannot change "Require password after scr… - Apple Community

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