Or North By Northwest where the villains sidekick says he "can't see the attraction" of the heroine. Or craziest (because the plot doesn't make much sense unless you manage to decode the hint) "A Streetcar named Desire" where Blanche drove her husband to suicide because "he was sensitive and liked poetry".
Or 'The Seven Year Itch' when Marilyn Monroe's character comments that the two men living upstairs from her are interior decorators and probably not interested in her.
Any portrayal of homosexuality on mainstream television in the 60's would have to be extremely subtle. We're already looking at an unstated rule in movies and television by that point that the Asian character never gets the girl. Making Sulu/Takei more open about his sexuality only compounds one unfair stereotype with another and the net result is even less progress: homosexuals are promoted at the expense of Asians (who, as one previous poster commented, finally had a truly heroic character in a major television program). And of course the network absolutely
will not sign off on it, for fear of losing sponsors and affiliates. Money talks, compelling storylines and social progress be damned.
If the Star Trek revival that was planned in the late 70's had actually come to pass, then there might be more of an opportunity to bring Sulu out of the closet since the Stonewall riots had happened and the gay rights movement had already started in full force. A savvy network executive might even see it as a smart marketing move to draw in a demographic that tends to be affluent for the advertisers. Even then the portrayal would have to be subtle to make sure the affiliates don't jump ship. TNG and especially the later series had a much better shot at pulling it off and it's still possible to retcon Sulu as gay with the Star Trek reboot coming up. Enterprise tried but it was clumsy at best (in fitting with the series as a whole).
That said, I wonder if there weren't some subtle hints in some episodes. Sulu's bare-chested fencing was already mentioned. But what about his sadistic alter-ego in 'Mirror, Mirror'?
(on another note, Ray Bradbury producing Star Trek would have been interesting. The writing would have been a lot better in the third season, at least. With Isaac Asimov as a science advisor for some episodes, Harlan Ellison and Theodore Sturgeon turning in scripts and Robert Heinlein promoting the show favorably and giving tacit approval for a borrowed story idea in another script, I'm surprised Bradbury
wasn't on the roster!)