Same issue here, using vSphere 6.7.
The Web Client works fine on Chrome 67.0.3396.99 x64 build, and IE11 on a Windows Server 2012 x64 acting as a workstation.
However, FireFox .52.0 x64 will exhibit the "cannot type " behavior.
Quick fix:
Uninstall FireFox x64 and install the x86 version.
The vsphere 6.5. and 6.7 authentication plugins will not work with FireFox above version 52. I spent hours on this, trying a couple of tricks like installing the vCentar root CA certificates on the Windows server workstation. Nothing worked for me.
That said, the authentication plugin works just fine with Chrome 67.0.3396.99 x64 and IE11,