VPN, CISCO AnyConnect, Mac OS X Version compatibility
The current version of the Cisco AnyConnect client available through WebStore (4.6.00362) is officially supported and compatible with Mac OS X versions that support 64-bit applications including Mac OS versions 10.11 (El Capitan), 10.12 (Sierra), 10.13 (High Sierra), and 10.14 (Mojave). As a 64-bit application, this version should be compatible with future operating systems Apple releases.
Is the Cisco AnyConnect VPN compatible with Mac OS X El Capitan (10.11)?
Mac OS versions older than 10.9 are not supported. The AnyConnect software versions needed to use Mac OS 10.8 or earlier have known security issues and are no longer being updated by Cisco.
Additionally, when you connect to campus with the VPN it is the same as if your computer is attached to the wired or WiFi network on campus. The campus acceptable use policy applies to any computer connected to campus, and requires the computer to be running an OS currently supported by the vendor. Apple normally only provides security patches for the three most recent versions of their OS. For example when Mac OS 10.14 came out, Apple stopped patching Mac OS 10.11, and only provides security patches for Mac OS 10.12, 10.13, and 10.14 so no computer with older software should connect to campus via the VPN.