I work in one of the most "green buildings" in San Diego on Ridgehaven Ct. I have been told a couple of times that my dog is not allowed in the green building because of her dander. Is that true?

If thats a rule they have for that building. 

It has nothing to with how the building was built.

Part of LEED certification requires certain air quility standards to be met. If the powers that be in your building are worried about dander infiltrating the HVAC system or getting in the carpets...etc, that is the only reason I can think of.

I think you need to follow the rules of green building. This is the only solution in my mind.