Symptoms:
This issue is resolved in VMware vCenter 6.7 U3g.
Workaround:
Or
Or
Or
C:\Program Files (x86)\VMware\Enhanced Authentication Plug-in 6.7
WindowsAuthKey_x64.reg
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\VMware, Inc.\CIP]
"UseSmartCardPrompt"=dword:00000001