OTL, the first US state to decriminalize consensual sodomy was Illinois in 1962, while Britain did so in 1967; the US and UK were unusual in this respect, since much of the rest of the world had made these changes to their penal code throughout the larger 19th Century (1791-1917). In a manner of speaking, the Anglo nations did not catch up to the rest of the world in terms of lgbt rights until the 1960's, generations after decriminalization as such managed to be un-controversial for most everyone else.
So what needs to happen for to shrink this gap, preferably considerably (by at least 30 years, preferably more)?