I'm not an expert on Turing but I do have a pretty high level of the history of homophobia and I can extrapolate from that. I think you're unlikely to find an answer other than homophobia exists. It was illegal during Turing's life, the consequences of being a known homosexual were significant, he was in fact chemically castrated as punishment for the crime of being a homosexual which he chose as an alternative to being imprisoned. Being confined in an insane asylum or treated with aversion or conversion therapy (which often amounted to torture - common "aversives" used in those kinds of therapies were things like watching homosexual pornography while receiving an emetic (vomit inducing) drug, an electric shock, or some other kind of significant physical pain so that the suffering of the aversive becomes indelibly linked with the homosexual desires in an attempt to "cure" those desires, "corrective rape" was also common) were also options for convicted homosexuals. The legal consequences were bad and the social consequences were just as significant. People would often lose their jobs, their standing in the community, their friends, their families, they could legally be disowned and thrown out of their homes, It was just so bad.

It can sometimes be hard to imagine what living in that kind of environment could be like but the intensity of the punishments for being a known homosexual, the way it could, would, and did truly ruin a person's life was very very real. So imagine if you were a genius of some sort and you knew that the only way you could actually live that genius life is if you lied and pretended you weren't gay. Turing grew up in that world and he knew what the consequences were and there just really is no way that didn't affect him. There's even a term for it called "vicarious reinforcement" which states that when we see others experience consequences for something (be it reward or punishment) we internalized that lesson as though we were the ones receiving that consequence ourselves. It's an important part of learning for pretty much every organism capable of learning and Turing would have been just as affected by that as everyone else is. He knew the consequences for homosexuality and it is likely that proposing to a woman seemed like a sort of necessary thing for him to do in order to avoid those consequences.

TLDR - There was nothing safe about being a homosexual in his time legally, medically, or socially and it's just not likely that other closeted homosexual had their own sham marriages for their own personal safety but Turing tried his own version of closeting for reasons other than as a response to the violent and dangerous homophobia of the time.