B737-800 flight crew reported right main tires flattened during taxi. Passengers were deplaned and Maintenance attended the aircraft.

Narrative

We landed normally on XXC. It was one of my best landings. Seriously. It was eye-watering. Even some of the deadheading pilots commented favorably.The headwind component was over 15 kts. and I used flaps 30 and brakes 2. The runway was dry and I disengaged the autobrakes below 100 kts. and slowed to below 60 kts. before exiting at the 1 highspeed. We continued on the taxi route to get to the ramp.As we were taxiing south on 2 and approaching 3 we noticed a CRJ ahead of us on 2 that was stopped in the middle of the hold pad. Trucks were parked near its two deflated right main tires.We were instructed to use 3 to join 4 southbound and continue to 5 to enter the ramp. As we passed the CRJ we started to feel the taxi becoming rough. I stopped the aircraft on 4 just north of 6. Another aircraft announced on ground frequency that we had flat right main tires. We contacted Ground Control and Operations for assistance. The APU was up and running and we shut down both engines. I didn't set the parking brakes and did ask for an airport vehicle to check the temperatures of our tires. An EMS vehicle said our tires were 120 and 160 degrees which was cool.Port Authority vehicles arrived on the scene and ordered some people-mover busses. Equipment for unloading baggage was also requested. The crew and passengers were transported to the terminal in those buses. The aircraft was left with the APU on and with Maintenance attending to the right main gear. Port Authority vehicles and personnel also stayed with the aircraft.Cause: I have no idea what caused the tire ruptures. Taxi speed was normal and the OAT was 4C. Could we have encountered the same thing that the CRJ did? Possibly; but another vehicle did a cursory check of the taxiway and didn't find anything. The tires looked like they were more shredded than punctured.