CDP is Layer 2 so I'm not sure why it would be put into the VPN tunnel in any case. Even if you had the "Any network" (0.0.0.0/0) in the VPN site, meaning all traffic is sent into the tunnel, that shouldn't cause this. The VPN client inserts routes into the client machine to determine what traffic goes into tunnel, and Layer 2 traffic is not routed.
If you're running an older VPN client version I'd first recommend upgrading to latest, currently 5.4.3. As next step I'd recommend opening a support ticket if the problem continues.
I'll try a new version (use 5.3.1)
as soon as you launch the client (connection is not established) cdp packet not sent into Ehernet, disable VPN client - cdp sent Ethernet (used for debugging Wireshark)