Collider wrote...
Well for one thing, the genophage was sanctioned by the Citadel. For another, the Salarians (presumably) had a seat on the Council, so something of the magnitude of removing them from the Council could be very costly politically. The Quarians did not have as much political power (probably partly because of their relative handicap for expansion - due to their immune systems), so it was easier for the Council to abandon them.
Interestingly, the Salarians created the genophage, but they did not use the genophage. It was the non-Council Turians who did. Kind of a backdoor deal, I suspect. You unleash a biological weapon. We'll give you a seat on the Council.
Not sure what role the Quarians ever had in Citadel space. Didn't take much for the Batarians to wash their hands of the Council, and the Council didn't seem too bothered seeing them go. I imagine there are dozens more spacefaring civilizations throughout Citadel and Terminus space that we never see because the developers didn't feel like designing dozens of aliens. Quarians might have been small time, not a loss to the Council.