I once read a book that suggested that the reason that Ludwig never married and built French-style gardens and salons in his palaces was that he had a sort of fixation on Marie Antoinette, despite the fact that she was killed before he was born. At least that it seemed to be a popular belief at the turn of the last century... he was also being described as "gloriously mad", rather than dangerous or subversive.
While it is interesting to speculate, what we would obviously interpret as homosexual or whatever is applying a modern lens to past events. Maybe Ludwig was a prototypical D&D nerd with the money and power to make his fantasies real. Maybe he was on the autistic spectrum, and being around people of the opposite sex made him uncomfortable. Maybe, as another poster suggested, he was asexual - though perhaps his "sinful desires" refer to autosexuality (unattracted to anyone but himself. Last I checked, that was frowned on too in the 1800's). Maybe he was impotent, or maybe he was somewhat agoraphobic. Maybe he was heterosexual, but was gynophobic. Flamboyant design taste is not necessarily the best indicator, or the Sun King was definitely very g*a*y. Not to mention Elvis Presley.