Air carrier Captain reported they had to come to an abrupt stop while taxiing to avoid another aircraft.

Narrative

After landing on runway XX L in ZZZ; we were instructed after clearing XX L to hold short of runway XX R on Taxiway 1. While holding short of XX R on Taxiway 1; an aircraft departed that runway; at which point we were cleared to cross runway XX R and contact ground. As we begin to clear the active runway; we noticed an aircraft off our left side on taxiway 2; approaching at a high rate of speed; which was an ERJ175. We were not certain if the aircraft was going to stop as their speed increased as we approached the edge of the runway onto the taxiway and had to come to an abrupt stop as that aircraft again increased speed to cut us off. We waited for that aircraft to pass us. We made a right turn on Taxiway 2 and contacted ground. We gave them our gate and we were instructed to taxi to Taxiway 3 for our entry point. I queried the ground controller as to the flight that had just cut us off; concerning their flight number. The ground controller gave me his flight number; and I said thank you and moved on to taxi to the gate. I commented to the ground controller that what that aircraft did was uncalled for in cutting us off as FAR's dictate when an aircraft is crossing an active runway to exit; it has priority and right of way over other taxing aircraft. We were left stopped with almost our entire aircraft blocking runway XX R for approximately 30 seconds. I don't believe there was any issue with the ATC controllers because we were crossing with the tower controller and told to contact the ground controller.