Stanford has gender-neutral restrooms throughout our campus, both in the areas that are exclusively for the community - such as in dorms - and for publicly accessible areas. People actually seem to prefer them. Men because they provide a higher level of privacy than in single-gender restrooms, since there are no unenclosed urinals, and women because the lines tend to be shorter. It does require a bit of mental acclimation, though.
Since the 1990s some colleges have had coed bathrooms on dorm hall floors, so it's not an entirely new concept, but is one that is labeled differently. My stepmom graduated from college back then and said she lived in coed on-campus apartments and dorms that had coed bathrooms. Perhaps because it didn't come with any form of label, such as "gender-neutral" or or with the public divisiveness of now, it generated far less of controversy. The layout most often used is a central area with sinks, and then on either side of it stalls with commodes and cubicles with showers. To me, what's most important is a stall or cubicle door that affords privacy and properly locks. The gender of the person barging in on me because of a defective lock is entirely irrelevant.
To add - I've seen many histrionic threads on here to the effect of "Obama wants our teenage daughters to share bathrooms with men! Oh noes!" I'm a teenage woman who shared a bathroom with many men every day last year (this year I'm interning and living off campus), without even the slightest bit of detriment. I never saw the genitalia of either gender because everyone used individual stalls, and not once did I ever feel vulnerable or compromised.