Race would be too hard because the non force sensitive class stories weren't written for that. Imagine if right after General Garza promotes you she points out that droids can't hold rank in the Republic military.
I've long wanted a droid class or two though. It seems like the common criticism that always comes up is "droids aint got no free will they just machines," but SWTOR, Star Wars in general, and Bioware (in the Mass Effect series) have covered that topic many times, so it wouldn't be too hard to write.
The biggest problem I see with droid classes is that the current generic planet quests are written for Jedi/Sith/Soldiers/Agents/Smugglers/Bounty Hunters, and NPCs often address you by title. I'm pretty sure it would be impossible to bring back every voice actor and have them redo lines to include droids. I think the only solution to that problem is to copy G0-T0's style from KotOR II and have the droid characters "place a holocall" and have a Sith/Jedi hologram standing next to them. The Jedi/Sith would be fake, just like how G0-T0 pretended to be a man remotely controlling the droid when he was actually the droid. The NPCs would address the hologram as if it was a person, and call them Jedi/Lord/Darth etc. Droids would also have to be restricted from the flirt options, because you can't really pull that off through a hologram.