Does anyone have a security program recommendation that is compatible with Catalina OS?

Apple's in-built protections are very good. No anti-virus program should be installed our used. They can, and do. cause problems. They will also slow down your computer. The other advice given here is excellent. If you must have an anti-malware app you can download and install Malwarebytes. It is safe and recommended by Apple's techs.

I and others use the in-built anti-malware.

Start reading here for some background: Effective defenses against malware and other threats - Apple Community

More than a little of the available anti-malware is uploading and re-selling your activities, and some of it is actual malware.

Also see: https://www.apple.com/lae/macos/security/