The problem has been solved following this thread:
https://communities.vmware.com/message/2691990#2691990
The solution:
In the home fodler of the user who's connecting via vmrc onLinux to the vCenter/vSphere and VM, one has to edit the file
~/.vmware/preferences
and add the follwoing lines:
usb.generic.allowCCID = "TRUE"
usb.ccid.disable = "TRUE"
With these addons, now vmrc on Linux (RHEL 7.6 in my case) is presenting the SC reade as expected.
A more general solution using /etc/vmware config golder is still in progress.