Why does System Preferences open, to the Finder Extensions pane, at startup?

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Does the issue present in this mode ?

3 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

4 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

5 - If the issue is present in the dummy account - then, this appears to be a System Wide issue on the computer.

Understand, we are all working Remotely from all around the world. 

Therefore, we do not have the On-Hands experience the User ( you ) has with this computer.

The next best thing for us to having a semi - actual On-Hand experience on this computer is to follow the steps below

Download the Application Etrecheck directly from the Developer.

The application is free or paid from added features. 

It will take a Snap Shot -  both the hardware and software.

 The Report will Not Reveal Any Personal Information. 

Post back the Full Report - copy and paste - using the Additional Text Icon ( 3rd Icon to last )

We can have a look at the report for possible issues and may have possible suggestions to resolve the issues.

Any Third Party Applications that will interfere with the normal operation of the OS,  is an invitation for disaster and comprising the Operating System

Certain Applications maybe available on the Apple Apps Store - this only means the Developer is prepared to pay Apple a portion on each sale. What the Application may do to the computer is up to the User to check this out before purchase

Any of the below should be removed as per Developers Instructions 

This will include CleanMyMac , This will include BitDefender , 

This will included Norton Antivirus , Sophos Av Software

Intego AntiVirus, McAfee, MacKeeper, Avast AntiVirus

Ad Guard, Webroot , ESET , Avira

The The Built in Security  is all that is required.

Interesting that you suggest this, because *another problem is that I have not been able to restart in Safe Mode. No way, no how, finger gymnastics notwithstanding—my computer *always boots in Normal Mode.

Use a USB Keyboard - simple and not expensive.

Can even borrow one or use a MS Windows Keyboard

There has been sufficient advise offered for the User to make an informed and educated choice what the next course of action is required for this computer.

The suggestions have been put forth on a volunteer basis, in good faith and in the best interests of the computer.

Then this computer needs to be Evaluated be an Apple Authorized Service Centre or an Apple Genius Bar

The is nothing more I can offer that this time.

Unless there is some other agenda a foot

Was System Preferences Open or active when the computer was shutdown ?

Was the tick mark in below Enabled

Is System Preferences set to Launch when the Computer Starts from a Cold Boot ?

Thanks for the quick reply, and for your help.

No, System Preferences was not open at shut down, and "Reopen windows" was not selected.

A mystery...

No, my only startup items are Google Drive, Dropbox, and yKey.

Good suggestion. One of the first fixes I tried. I've used wired and wireless, three different keyboards. Still can't boot in Safe Mode. I basically gave up on that.

Thank you for your advice.

Have a nice day!

Welcom and you too