MacOS Catalina Security & Privacy Window Keeps Appearing at Logon/Startup

Verify System Preferences are not in the log-in items for some reason.

>System Preferences>Users & Groups>select your account Log-in Items

unlock the pad lock to make changes. Use the - (+/-) to remove items from the list

If no change, to get a good look at your System config. for conflicts or issues, you can run this utility http://etrecheck.com

If you need help interpreting the report you can post it here in its entirety in the "Additional Text" box in the editing toolbar below, in your reply.

You can set its preference to "Allow full Disk Access", with this you get a digest of issues from the last 7 days that are saved in your system.

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Other option might be to try a SafeBoot to clear system caches in an effort to resolve: SafeBoot https://support.apple.com/en-us/HT201262

Takes noticeable longer to get to the login screen, does a 5-15 minute disk repair before it fully boots up, and certain system caches get cleared and rebuilt, including dynamic loader cache, etc. Login and test.