In this case, _the_ difference is that Saudi Arabia has never been a liberal democracy. America hopes it's relationship with countries like Saudi Arabia helps to liberalize them. In that regard, Saudi Arabia is liberalizing, albeit very slowly. Just look up women's rights.
As for homosexual rights, that tends to be a religious issue that many Muslim countries have an unfortunate record of oppression on. America's freedom of religion tends to be tolerant of these people, even though its antagonistic to our liberal values.
Who are "they" and "the US" here? I guess you are referring to the political elite. I rather not have someone else force me to boycott whatever they think they have a feud with.
US foreign policy is 100% not about this. If the US had no economic interests in keeping Saudi Arabia on its side, it wouldn't happen. That's all our foreign policy is about and lofty goals like this only matter if there's no economic interest.
As a 3rd world spectator I only have to say "it's about time"
American foreign policy tends to be fairly uniform this way, no?
If Iran released prisoners and held open elections, I suspect American would move to lift embargos and normalize relations. Same with Caracas, et al.
To see this play out in real time, watch Niger.
Currently, the US backs a handful of dictatorships, of which some are former democracies. Egypt may be an example of former democracy, albeit flawed, turned into a military dictatorship. And among de facto dictatorships that the US still maintain perfectly open relationships are Thailand, Myanmar, and Morocco.