The issue regarding loading is the same for the various types of tires.
Well tire experts (rvtiresafety/experienced RVers and Goodyear disagrees.
Goodyear Tire and Rubber .... weighing RVs
Special Considerations
Unless trying to resolve poor ride quality problems with an RV trailer, it is recommended that trailer tires be inflated to the pressure indicated on the sidewall of the tire. Trailer tires experience significant lateral (side-to-side) loads due to vehicle sway from uneven roads or passing vehicles. Using the inflation pressure engraved on the sidewall will provide optimum load carrying capacity and minimize heat build-up.
*******************************************
Now for a better understanding how tires on a trailer need different air pressures, than a truck or motorhome/car/suv/etc, requirement read this tire engineers website. Roger (Tireman9) has pages and pages of trailer tire tech info for newbs or even uneducated tire dealers.
http://www.rvtiresafety.net/2013/11/interply-shear-and-other-techno-babble.html. He has pages and pages on the subject.
The OP asked; Do I need D tires?
I sure wouldn't.