That's exactly the problem with the MU as seen in DS9. The writers apparently got the idea that it should just be an opportunity for some silliness, dressing up and girl on girl action - and who cares if it makes any sense.
It doesn't make any sense in TOS either. It just doesn't make sense in a different way.
In what way it didn't make sense in TOS?
Some things obviously didn't make sense - like Kirk and co. finding themselves in an alternate universe and immediately having different uniforms.
One might say that's also very unlikely that same people would get conceived and born in an alternate universe, i.e. that the combination of chromosomes from their parents would be exactly the same (or even that their parents would all have mated in that universe as well)... which is the problem with most alternate universe stories. But it's hardly the only thing in Trek that doesn't make sense scientifically, there have been many worse offenders in that regard (galaxy populated mostly by humanoids? Very different humanoid races being able to have children together? A nearly infallible UT? etc. Not to mention the spores from "This Side of Paradise", Kirk's transporter accident in "The Enemy Within", B'Elanna being split into her Human and her Klingon half, and so on).
But dramatically, as a story, it did have a point. It introduced the idea that, in an alternate universe where things had gone very differently, Human society in the 23rd century was one built on ruthlessness and conquest; and under those different circumstances, Our Heroes could turn out very differently. It's basically a look at the dark version of the Federation, and what kind of people would the main characters we know and presumably love be, if they were brought up and lived in a universe where the strongest and the most ruthless survive.
It's fantastic premise, IMO. But Trek fiction, canon and non-canon, has dealt with it with mixed results. The best stories have been those that took the premise seriously. The worst were made when the writers seemed to stop taking it seriously and made it an exercise in silliness.
I'm going to have to rewatch some of these episodes, but what are we really talking about here other than the Kira/Ezri kiss in one of the later seasons? Is the Intendant even portrayed as bisexual before that point? I seem to remember her draped over a number male consorts and lusting after mirror Sisko primarily. She fawns over Kira when she first arrives, but that is an expression of her narcissism, not her bisexuality.
Maybe I need to rewatch the episodes, but I seem to remember that she had female sex slaves as well as male.
By the time Kira and Ezri kiss in season 7, two women have already kissed in the main DS9 narrative, so it's not as if this behavior was only conceivable for the show within the "depraved universe," though I agree wholeheartedly that Trek should have had an openly gay character by this time.
I don't think the DS9 MU is primarily the "evil bisexual universe." It's just a universe where anything goes to a certain extent, such as Sisko sleeping with Dax and so on.
Kira and Ezri, and Ezri and Leeta. So that's 3 female characters who are straight in the prime universe (it would be far-fetched to postulate that Kira was bisexual in the PU, for instance), who are bisexual (Kira), lesbian (Ezri, as suggested by Mirror Brunt's comment), and either bisexual or lesbian (Leeta). Also, the writers never wanted or allowed 'prime' Garak to be bisexual, even though Andrew Robinson played him that way at first (in his own words, he saw the character as omnisexual), and even though many of the fans thought he was bisexual or gay; but they had no problems with having Mirror Garak make a pass at Regent Worf. When the prime universe does not contain any gay or bisexual characters (Jadzia Dax comes the closest, but even in that case, she is attracted to another female Trill because of the memories of one of her previous male hosts - the feelings come from the symbionts, whose previous hosts were husband and wife), while several of their Mirror counterparts are shown engaging in homosexual relationships/sex/flirting... it leaves a bitter taste and invokes the aforementioned "unfortunate implication" that homosexuality is something that people do in a world without moral rules, where "anything goes".
I loved all of the Adama breaking down scenes. They were all so heartbreaking and moving. I felt so much sympathy for the guy every time and at the same time was really impressed with how fascinating the performance was, so I could appreciate it on several levels. 
