Yes, 360 Security causes issues with Fences.
It's interesting that you say that. I also had 360 Total Security installed recently, and it detected a problem with a non-Stardock program (Better Explorer). I wonder if the issues above are not actually related to Stardock but could be a ransomware problem. It can cause fake warnings. Ransomeware can take control of the PC disabling users to do things like open certain files and folders, cause programs to crash, and other harmful things.
Also, I had Fences and 360 Total Security installed at the same time, and I never had any problems with Fences.