The thing is, I reckon that the nastiness would be pretty bad with a divisive character for a long time after the 19th century was over. As a hypothetical, opinions on Carter and Dubya (to pick two at random) are somewhat divided. Not to Buchanan levels, but both have a fair bit of hate. If either or both of these were homosexual, bisexual or anything else, their failings could be blamed on this "deviancy", and equally all of similar orientation would be seen as having the same failings*. Ladd coming out posthumously heavily implies that TTL isn't ready for such a president in the late 19th/early 20th century. I'm doubting whether OTL would be ready for such things 100 years later**.This is why a Buchanan analogue AH would not work, as he happened to end up considered divisive and indecisive at precisely the wrong time. He's now generally considered the worse president OTL. Unfairly as it obviously would be, his shortcomings as president would have been twisted in all sorts of ways in the late 19th Century around his sexuality. Probably for the best that serious speculation was held off for a century or so.
*Probably only by a vocal minority, but they sure would be vocal.
**Not just the US. I can't imagine that the thought of an openly gay or bisexual British Prime Minister would play any better...