Do Tamper resistant receptacles violate ADA barrier-free requirements?
No, for several reasons. 

To the extent there is a conflict, there is no conflict.

State laws adopt NEC.  ADA is a Federal law.  Federal law preempts state, as was decided at the Appomattox Court House in 1865. 

The essence of ADA is You must do what is easy.  That never goes away, but a few things are specifically exempted, including how single family homes are constructed.  The core rule still applies, for instance, to a landlord renting to an ADA tenant.  

NEC does not require ADA-inaccessible sockets

NEC requires listed tamper-resistant receptacles.  They delegate the definition of "tamper resistant" to Underwriter's Laboratories.   

It does not require they be frustrating and difficult to use; that is decided by the individual manufacturers, and to a certain extent the UL's testing rules (which may be a place to make some legal progress). 

Not surprisingly, cheap ones are cheap.  You can't just grab a terrible one and go "See?" You must make a reasonable effort to find a quality unit, or show that the nature of UL's certification process makes that unlikely.  It's on you; you're claiming tamper-resistant receptacles are not accessible, and bold claims require bold proof. 

Be prepared for compromise

The people enforcing NEC are your local electrical inspectors, which NEC calls  the AHJ (Authority Having Jurisdiction).  Be prepared for some back-n-forth with them.  For instance the AHJ may borrow a page from NEC 517.18C and allow a tamper resistant cover.  

As long as they can come up with a reasonable way to comply, you probably wouldn't be able to pop an ADA exemption.  This is where ADA works against you: You must do what is easy.