I don't think RAH can be called a conservative other than in a fiscal sense.
Anybody so obviously fascinated by gender-switching, homosexuality, incest and other interesting sexual variations doesn't fit my definition.
Don't be to hasty in that conclusion. In his youth he associated with a group of people who shared an interest in such topics. Few people remember Aleister Crowley today, but Jack Whiteside Parsons was the founder of Jet Propulsion Labs.
I think, in the same way that some will define "justifiable" homicide, Heinlein delved into societal abnormalities where "justifiable" alternatives to traditional mores seemed excusable.
But if he ventured into actual homosexuality, he must have done it in such a gentle fashion that I hardly noticed.