Turing's destruction is more complicated than just prosecution by conservatives. He had access to extremely secure information over a period of years, this is what drew attention to his homosexuality.
When someone gets a security clearance, what do you think is looked for? Not many spies or people who eventually divulge information to an enemy country have explicit ties, eg. they aren't a member of a communist party. What is investigated are characteristics that would make a person likely to be influenced: debts, addictions, gambling problems or, as in Turing's case, some sort of socially unaccepted lifestyle.
Around the time of Turing's conviction, several other homosexuals had been convinced by the soviets to become double agents, eg. Anthony Blunt and Guy Burgess. Turing also made regular trips to the continent to pursue sexual relationships. This is what inspired the indecency charges. That's my understanding at least.
Please understand, what happened to Turing was terrible. No one deserves that fate. I really do wish he could have escaped somehow. That said I don't think the situation was as simple as social conservatives destroying people.