One reason Chalmun’s Cantina was so popular among spacers was the droid detector that Chalmun installed in the foyer. For a long time, Imperial Sentry Droids made private discussions between smugglers and crime bosses all but impossible. While the detector didn’t keep the Sentry Droids out, it did warn everyone that their activities and discussions were about to come under Imperial scrutiny. This enabled everyone time to compose themselves and present a perfectly innocent demeanor. Chalmun’s also had a strict “No Droids” policy to prevent people from bringing their own droids into the Cantina with them.
Via Reddit, where a commenter suggests it could also just be that since droids don’t drink they’re wasting space for customers.