Several weeks back there were a couple of questions from our field asking about locking down access to a Virtual Machine's Console which includes both the new Standalone VMRC (Windows & Mac OS X) which runs on your desktop as well as the new HTML5 VM Console which runs in the browser. Below is a screenshot of the vSphere Web Client showing how to access the two different types of VM Consoles.
To prevent users from accessing either of the VM Consoles which also applies to the vSphere C# Client, you can leverage vSphere's extensive Role Based Access Control (RBAC) system. The specific privilege that governs whether a user can access the VM Console is under VirtualMachine->Interaction->Console interaction as seen in the screenshot below.
If a user is not granted the following privilege for a particular VM, when they click on either the Standalone VMRC link or the HTML5 VM Console, they will get permission denied and the screen will be blank. Pretty simple if you want to prevent users from accessing the VM Console or allowing only VM Console access when they login.
UPDATE (12/15/15): If you want to restrict users from having ONLY VM Console access which may include the Standalone VMRC, you will need to ensure that the user has the role applied not only on the VMs you wish to restrict but also at the ESXi host level since Standalone VMRC still requires access to ESXi host. You do not need to grant read-only permissions for the user at the ESXi level, but you just need to assign the user "VMRC" only role at the ESXi level or higher to ensure they can connect to the VMRC.