Is it possible to automate changing some security settings in Catalina? I realize the user would have to enter their password, but beyond that step could the process of adding a program to Accessibility, Full Disk Access and Screen Recording be automated in some way? Programs like Teamviewer and Splashtop (to name two that I know of personally), require the user to make these changes before I can provide remote support. This is a bit much to ask of people for whom minimizing a window is a challenge.
BTW, the Macs in this situation are not part of an organization; they are individually owned Macs that could be anywhere in the USA.
Yes. Set up a MDM and you can easily make configuration profiles so your peers or people you support don’t have to manage their Macs as much.

https://support.apple.com/guide/mdm/welcome/web
https://www.apple.com/macos/server/
https://www.fleetsmith.com/ or https://www.jamf.com/products/jamf-now/