That doesn't change the fact, that they still legally citizens, law says one thing, societal and cultural-born prejudice and speciesm says another but law is above the latter.
If you need explanation: Perhaps among higher social classes, due to influence of Jar Jar, Droid personhood started becoming popular idea, if only to appear progressive. In turn, planetary nobility and rich indirectly influenced public perception in the campaign or Pro-Droid Senators did. Perhaps it was dumb luck-for example, no one noticed that candidates were Droids due to sheer disbelief. Perhaps they won as a joke, in real-life, people made political parties as a joke and people still voted for them, perhaps this is similar situation with the idea of Droid Supreme Chancellor being so amusing that in twist of irony, it become the most popular option for people to vote and won.
Either way, legally, Droids are people, legally they citizens and become Senators and Supreme Chancellor, even if in public perception they still objects and discriminated against, law allows them to accomplish Chancellorship so stroke of luck is all Droid candidate needs and this is all the explanation we need as the quest participants. Jar Jar Binks was also unbelievable and in-universe he didn't even start his own campaign, people just voted for him.
Also, in all respect to my boi Tarkin, he is the boring choice and Droid Chancellor perfectly encapsulates the changes and hope, Binks brought for the Galactic Republic and Galactic civilization as a whole, so even if extremely unbelievable, it's thematically good.
Also, personally I don't like expies either and I prefer Venari or C-3PO, but Droid Chancellor is Droid Chancellor for me.
