Peter Bogdanovich's quoting Welle's telling him about Houseman being gay (and enamored of Orson) seems quite suspect to me.
One reason I really don't think it's true, is because there is little doubt that Bogdanovich took on Welles own dislike of Houseman, blaming him for supplying Pauline Kael with all the information about Mank being the only one to write the script to KANE. Bogdanovich now says he even didn't like Houseman when he first met him as a young actor at the Stratford, Conn. Shakepeare Theater in the late fifties.
But as Houseman tells his version of their break-up in RUN-THROUGH, it's clear that their Mercury Theater producing partnership couldn't last in any event. It's also interesting to note that in Callow's new book, Orson seemed to tell all his close male friends how much he loved them, and seems to have inspired love from them in return... all strictly platonic it would seem.
But in any event, even if Welles felt betrayed by Houseman in some ways, in reality, I would say Welles would be more at fault, and also the bigger loser of the two in their break-up, since Houseman seemed to function quite well as a leading Hollywood producer with directors like Nicholas Ray and Vincente Minelli. As Glenn has noted, Welles would have fared much better if only Houseman has stayed around and handled the money problems and deflected the interference from the studio that he proved to be so good at with his films with other iconaclast directors, and as he did with Welles, allowing him to function at his peak on their stage collaborations.