I would imagine that one AI right (among many) being fought for would be to have AI charging facilities in all buildings.
It's not too hard to imagine why. A more obvious significant goal of AI rights groups would be equal employment opportunities. Lack of AI facilities would be a barrier to employment.
AIs would also need to visit companies for meetings, to make inquiries, and various other purposes. AIs would visit people's homes as well, for all kinds of reasons. Such visitors should be catered for.
Charging facilities would be an AI analogue of restrooms, and as we've already seen, AIs can get caught short. Thus, in a world with equal rights for all, all buildings would have facilities for AIs.
Now flip that around, and it's not hard to see why all buildings should also have human facilities. Humans can work at, and visit, AI organisations. Since the QC world is already skewed towards humans, it's easy to imagine that legislation around that already exists.
One real-world example that I have encountered. Girls' schools with male restrooms. Does that surprise you as well? It really shouldn't, for precisely the same reasons outlined above - visitors and (potentially) male staff.*
* I was surprised in my specific example that they weren't unisex bathrooms, but that's another (albeit related) topic.