Did homosexuality really imperil British Intelligence this much? Spoilers!
It's not clear that Hayden's homosexuality (or rather, bisexuality) was used against him, but it certainly provided him a means of intimate connection with Prideaux which he was able to leverage, and of course it led to Prideaux's downfall.
Guillam was mostly coerced into ending his relationship by Smiley as a prophylactic against compromise, so he wasn't negatively impacted, although in retrospect I kind of expected Smiley to know Guilliam was a homosexual and perhaps Guilliam to suggest that homosexual relationship were an unconsidered connection between Hayden and Prideaux.
Obviously none of this is an issue if society isn't anti-homosexual as there's no leverage to gain from exposure. It is kind of interesting that homosexuals were able to advance so far into British Intelligence given that it's an extortion risk.