Hi Denis,
we had a similar thing happening here: Install eod :: mgm configuration
If i remember this correctly, the eos client itself will not work in this situation. We ended up relying on the xrdcp / xrdfs clients that do work fine with GSI certificates.
edit:
we also see the exact same error with the EOS client, i.e.
Unable to execute proc command - you don't have the requested permissions for that operation (1) /proc/user/; Operation not permitted
Best,
Erich