Droids probably maintain the same status as Holograms do in Star Trek: that is, questionable sentience on a case-by-case basis.
For a canon example, let's look at the two droids we know and love. C-3PO is a protocol droid, and although he has a well-developed persona, it's simply a programmed persona (let's blame Anakin for this one, he's the one who built 3PO). He may have developed a good relationship with Anakin, Obi-Wan, Padme and later Luke, Leia and, well, probably not Han, but he's never really shown to act outside of his programming. 3PO is the nanny, the straight man, the highly-phobic over-reactor, the linguist, the butler, etc. He's not a soldier (didn't quite work out that way in AOTC), he's not a diplomat, and he's not a scientist. Never have we seen C-3PO exceed his programming in a way that would display self-awareness.
On the other hand, we have R2-D2. It can be argued that R2 is sentient, however, and expresses this even despite his limited linguistic capabilities. It's clear he has not only an attachment, but an affection and compassion for the 3 heroes (depending on trilogy) and will go beyond his programming to help them. Remember, he starts out as a maintenance droid on the Naboo Royal Cruiser. But over the course of six movies and several TV shows, we see R2 act as a pilot, scientist, soldier, spy, waitstaff, messenger, saboteur, rescuer, engineer, etc. When R2 cannot do something, it is because his Human components already have, or his physical implements limits him (and this isn't often, considering his array of tools and extended programming). R2 also has demonstrated a clear self-awareness, not only in the face of refusing orders, but at the range of expression of demonstrated emotions.
Now, let's consider a piece of sweeping legislation to hash out the rights of both droids. How would you define the difference between C-3PO and R2-D2? Would you simply give both rights, and then be stymied by poor programming in a non-sentient droid? Or could you somehow have some metric, some technical test to determine sentient (and how would that come about, how reliable would that be, etc)?
I think broad legislation would be very difficult to enact, considering that most droids are thought of as simply servants and/or machinery. Very few have developed not only their own personality but their own self-awareness, enough to warrant such protection. It might simply be easier for the Senate to pass the issue along to the courts to determine on a case-by-case basis, a sort of Emancipated Droid status that could be applied for. This wouldn't cover every single sentient droid, but it would hit most of them (and could easily be a plot point for any PC droid who wanted to run with it) and that might be enough.
However, Mak, if you would like a Senator to help co-sponsor a bill to bring the discussion to the Senate, I see absolutely no problem with this. I'm not sure if Yora is the best one to do it, but there are a few other active Senators who might want to champion this cause.
tl;dr: I'm not sure if a bill would pass to grant all droids recognizable rights, but I see no problem with submitting it. The Courts might be another workable storyline for a case-by-case basis status.