Each cantina customer has a criminal record or weapon
Solo freaking shot a dude and some Jedi performed amputation
No one seems to give a damn, they just shrug and keep on drinkin'
Yet they deny entrance for the droids!

According to the official explanation, the dayshift barman's Droid intolerance was understandable. He lost both his parents as casualties to Separatist Battle Droids in the closing days Clone Wars.