Yes, it is, but I think the implementation matters. In my building on the Google Kirkland campus, we have men's and women's bathrooms in a few different places, and also one place where there's 5 single-occupancy unisex bathrooms and one mother's room. It's great! It doesn't take any space away from the other bathrooms, and it accommodates people who are uncomfortable in the cisgender multi-person bathrooms for whatever reason (maybe they're somewhere in the QUILTBAG or maybe there's totally unrelated physical or psychological reasons they prefer single-occupancy restrooms).
My understanding is that we're not trying to strike down all the barriers and make all toilets unisex, but there definitely are people who are working to make sure that every building has at least one of those unisex single-occupancy bathrooms, for people who need it. It doesn't cost Googlers anything except at most a couple of conference rooms.
As a primary-carer father raising a toddler I don't like that terminology. I'd prefer that they'd just call it a Lactating Room rather than trying to be coy and seemingly indicating a preference for one parent.
It's named a "mother's room" because it's for feeding/pumping, and so it's an attempt to offer privacy to people lactating. He's objecting to the name's failure to properly convey that, suggesting that (like putting changing tables solely in women's rooms) it reinforces the (harmful to both genders) assumption that childcare is a female task.
Which is to say - a "baby care room" is also a good idea, but it would be a room with a different use. The proposed name change was about making the name conform to the current intent of the room.
single unisex stalls are great because they also accommodate for people who prefer them for any reason, without out requiring political or clinical validation of those reasons.
My understanding is that we're not trying to strike down all the barriers and make all toilets unisex, but there definitely are people who are working to make sure that every building has at least one of those unisex single-occupancy bathrooms, for people who need it. It doesn't cost Googlers anything except at most a couple of conference rooms.