We were able to keep it open on the monorail, even when it was busy. We would have taken up just as much room closing it and removing all the bags and blankets and such, the station operators told us to just leave it and ushered people past our section. That was in Sept of last year.
The large boats from MK to WL allowed the strollers to be opened, regardless of the type of stroller (umbrella and regular sized ones too). The smaller, water taxi boats the strollers must be folded.
And the buses...my least favorite with stollers. It depends on the driver and time of day. We were allowed to leave the stroller open twice going from FtW to the Settlement ( we never left the resort on the bus), but after that, no way. Our last night, it was raining and late and the bus driver allowed us to leave DS stroller open provided it was locked. But again, it was late ( like after 11p) and really rainy. I think he took sympathy on us.
One driver told us that the driving regulations that apply to WDW will not allow strollers to be opened and have a child in them for safety reasons since they aren't really secured.