Can an app change the web proxy settings without user interaction

Have you installed or run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

There is a preference setting in Security & Privacy System Preferences, General, Advanced, to require admin password to access system-wide preferences. That might disable that for an app, but if you gave it an admin password, it would be able to authenticate.

Can an app do this without user interaction in System Preferences?

No, but when you entered an Admin password to the request to install the app, you gave it permission to change those settings.

Option # 1 - There are no known Windows-like Viruses in the wild that self replicate and affect macOS, because of the underling UNIX  Foundation and Permission Limitation. 

The The Built in Security  is all that is required to protect the computer.

Should “ Certain & Specific Software “ referenced from above be installed - it will negatively impact macOS. It is suggested, to download directly from a respected ASC Contributor, the application Malwarebytes for Mac. 

It is free or paid for added features. 

Disclaimer: I am not affiliated with nor receive compensation from the Developer.

Run the Application and it should remove the malware / adware. Once done, restart computer and test.

Option # 2 - Suggest downloading the Application Etrecheck directly from a well Respected ASC Contributor. 

Disclaimer: I am not affiliated with nor receive compensation from the Developer.

The application is free or paid from added features. 

Run the application with Full Disc Access ( Security & Privacy - Full Disc Access ).

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, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS.

This includes AntiVirus, Disk Cleaners, Disk Optimizes, UnInstaller etc.

The The Built in Security  is all that is required.

First, there is no reason to ever install or run any 3rd party "cleaning", "optimizing", "speed-up", anti-virus, VPN or security apps on your Mac.  This user tip describes what you need to know and do in order to protect your Mac: Effective defenses against malware and other threats - Apple Community.  

There are no known viruses, i.e. self propagating, for Macs.  There are, however, adware and malware which require the user to install although unwittingly most of the time thru sneaky links, etc.   

Anti Virus developers try to group all types as viruses into their ad campaigns of fear.  They do a poor job of the detecting and isolating the adware and malware.  Since there are no viruses these apps use up a lot of system resources searching for what is non-existent and adversely affect system and app performance.

There is one app, Malwarebytes, which was developed by a long time contributor to these forums and a highly respected member of the computer security community, that is desshoigned solely to seek out adware and known malware and remove it.  The free version is more than adequate for most users.  

Also, unless you're using a true VPN tunnel, such as between you and your employer, school or bank's servers, they are useless from a privacy standpoint.  Read these two articles: Public VPN's are anything but private and Former Malware Distributor Kape Technologies Now Owns ExpressVPN, CyberGhost, Private Internet Access, Zenmate, and a Collection of VPN “Review” Websites. 

Uninstall CMM according to the developer's instreuctions.

Any Third Party Applications that will interfere with the normal operation of the OS, alter, modify, remove or delete or attempt to do so is an invitation for disaster and may require a Reinstallation of the OS.

https://discussions.apple.com/search?q=cleanmymac The first 600 posting on this Application all pointed to remove as per Developers Instructions