I sill can't believe what happened to one of the most influential CS people of all times :-(
Well, I believe the authorities were more concerned about the perceived security risk. Male homosexuality was not decriminalised in England and Wales until 1967 (and not until 1980 in Scotland and 1982 in Northern Ireland). Before that there was the concern that someone like Turing could be blackmailed for state secrets (he played a key role in the wartime code-breaking effort).