I can see why you say that. This whole issue is edging towards a dark road, which is stepped upon once this question is asked: "Ancient Greece had democracy, which America has, and had a thriving homosexual subculture, which America has. Why is it that homosexuality and eventual pederasty end up coexisting comfortably with democracy?"
I'm just posing this question illustratively. It's not meant to be answered.
Accusing me of avoiding the issue that a society that gives the commoner a voice in the law can/will open it up to gross moral abuses?
One would think that Greece’s more naked democracy would have brought their ruin faster. But it’s the US with its supposed representative government structure that has the buggery and grosser practices. Maybe it’s technological, that ancient Greece never had a very good contraceptive, which kept gaydom from hiding away in a background of compromised heterosexuals who were afraid of being called hypocrites.
This question can be easily answered. Democracy gives people the tools to make their behavior legal.
The power of majority is not even required. It is enough to have some numbers to begin trading power. And that's what happens here. Often small but loud groups make themselves an annoyance, and the rest of voters gives them what they want just to make them go away (every child knows how that works.) At other times those groups recruit fringe media, mount propaganda campaigns, and basically mess with your head so much that you start believing that black is white - and eventually vote against your own interests.
A dictatorship (such as monarchy, for example) is not a guaranteed solution, of course. However monarchs usually outsourced morality to the Church, and the Church - represented by local priests - kept an eye on the situation. Not only the priests explained on daily basis why certain acts are sinful, they would also send a word upward the hierarchy if a new Sodom is about to occur. Then the King would send a few soldiers to arrest the offenders; their trial would be fast and definitive. But before that becomes necessary a bunch of villagers with farm implements in hand, likely led by the priest, would show up at the house of the offender and explain to him the error of his ways.
I mentioned that dictators are not a guaranteed solution. But they do help, for one simple reason. A dictatorship always needs warriors. A dictator wants a strong country that can defend itself and, preferrably, attack others. However a bunch of homos do not always make the army strong. The dictator also wants more children to be born, but gay families cannot produce children. Any dictator who runs a gay-friendly country is digging his own grave. Democracies, on the other hand, never think about the future - they have no built-in, automatic mechanisms for sacrificing something today for the greater good tomorrow. They can only depend on wisdom of voters, a fleeting thing.