I installed Cisco AnyConnect 4.9.04043 and 4.9.04053 on my second Big Sur test Mac, and have had no problems with either of my two Macs since last night.
What I did do, as part of the test, was to uninstall then reinstall Cisco AnyConnect again on each Mac, and fully complete the installation process (including allowing the system extensions).
Maybe the AnyConnect reinstall fixed the problem (and I reinstalled AnyConnect several times when testing), but I've had AnyConnect and SEP running for several hours, without any conflicts.
Here's a screenshot of my primary Mac. Again, please excuse the image, it was taken on a Retina display and I wanted to show as much information as possible:
I have a functioning Symantec Endpoint 14.3 RU1 on the left, with Cisco AnyConnect 4.9.04053 on the right.
As a more comprehensive test, I installed AnyConnect with every available option selected, and I did not disable or remove any of the Cisco AnyConnect Socket Filters from System Preferences -> Network, and I did not delete AnyConnect files from the the file system.
AnyConnect and SEP have been running side by side all day, with no conflicts reported.
Even after rebooting, AnyConnect and SEP do not conflict with each other.
The only change I have made since last night was to reinstall AnyConnect during testing.