Familial history mainly, I have a VERY large extended family so there are lots of experience to draw on for all sorts of situations especially the how too's and how not too's of raising successful independent children into adults. Not necessarily empirical and most definitely anecdotal, none the less seeing enough examples with close interaction over very long periods of time does give an insight to what is required for successful child rearing.
While definitely not as well read on the subject, (its not a favorite subject of mine though it can be fascinating in small doses.) my familial community and that's what we are a genuine community we are that large a family, have had some experience in these matters. We have found that heterosexual and homosexual parents are equivalently loving and genuine, and that up to puberty basically there is little if any difference or effect worth noting. The difference is after puberty were homosexual parents don't seem to quite relate as well heterosexual parents, to their heterosexual children hence causing more friction than would otherwise occur. Its a similar dynamic in a divorced household were only one parent predominates in the relationship with their children, though there are plenty of differences. We have our theories (many) as to why but sufficed to say that seems to be the consistent dynamic.
As to your empirical evidence, I am not convinced as to it's validity. As I said before your profession has a tendency toward fads and that seems to be a fad. It is also has much more art and subjectivity than the other more "robust" sciences. Until I see conclusive evidence to the contrary I will hold to my opinion, which I consider to be right. While you may consider me wrong, my opinion counts for the one person that counts, that's me. That's just the way I see things.