Mac Mini Thunderbolt ports to 2 Mini Display Ports Can the Thunderbolt ports on current (writing this question in March 2017) Mac Mini, drive two Apple Cinema Displays (which I believe utilize mini display ports?

I got contradictory answers to this at the local Apple store.
Yes.

According to Apple's own Tech Spec page for the Mac Mini it has


  Support for up to two displays at 2560 by 1600 pixels, both at
  millions of colors


Specifically with the Thunderbolt Port:


  Thunderbolt digital video output
  
  
  Native Mini DisplayPort output
  DVI output using Mini DisplayPort to DVI Adapter (sold separately)
  VGA output using Mini DisplayPort to VGA Adapter (sold separately)
  Dual-link DVI output using Mini DisplayPort to Dual-Link DVI Adapter (sold separately)
  


Keep in mind that Thunderbolt 1/2 is a "multiplexing" of DisplayPort and the PCIe bus on one cable.  This is why you can use native mini DisplayPort adapters in the Thunderbolt port.

So, as far as your two Cinema Displays, you just plug the each of the mini DP plug into each of the Thunderbolt ports and you're done.