As mentioned, I think there's some evidence of Garak being queer, but not a lot of Bashir. That's where fan theorising comes in. But even in fanon I don't think people thought they were "in the closet", ie hiding their sexuality. It was more a case of "what we see on-screen is not the whole story, the fun stuff happens when the cameras are off them".
This is similar to how a lot of fans saw Seven as queer (even though I personally don't think there was a lot, if any, evidence of it on screen). But there was sufficient momentum for this fan theory that the writers made Seven canonically queer in Picard.