I am aware of the picture of the man wearing the 'dress' from TNG, which promotes gender equality, but are gay rights ever addressed in Star Trek at all? (All seasons accepted.)
Takei said he spoke to Roddenberry about the possibility of broaching the gay rights issue, and Roddenberry seemed genuinely interested in the idea for TNG but passed on before he could implement it.
But the shows have touched upon the issue very subtly in some places, as outlined here.
For instance, Trill relationships have tangentially introduced non-heteronormative attraction as well as complex gender identities:
- Beverly's love interest, Odan, is later seen in a female host
- Dax obviously has been both male and female, and there are definite homoerotic undertones in her re-encounter with Lenara Kahn in Rejoined. To a lesser degree, her re-encounter with Enina in Dax also demonstrates a shared continued romantic bond with another woman.
(Jadzia and Lenara's kiss was apparently censored in several Southern states.)
And there's also the introduction of races with non-binary genders/marriages:
- J'naii, the asexual androgynous species from The Outcast, which Soren belonged to.
- Bynars, a genderless quasi-cybernetic race.
- Vissians, a species with 3 sexes and genders where the 3rd sex was treated almost like communal property that's passed around to couples trying to reproduce.
- Andorians, who—according to Data—require groups of four to marry. In canonical works, there have only been 2 genders depicted, but they could potentially have more than 2 genders, or 4 sexes and 2 genders (i.e. 4 different sets of plumbing, though only 2 culturally expressed genders).
- Bolians, who have 2 genders but sometimes marry in groups of 3 or more, as implied in Field of Fire when Ezri mentions that Petty Officer Zim Brott has a "co-husband" in addition to a wife.
And, ironically, the chauvinistic Ferengi race has also been used to explore trans characters:
- Quark gets gender-reassignment surgery in Profit and Lace.
- Pel is also forced to crossdress because of Ferengi repression of females.
There's also lots of homoerotic scenes in DS9 episodes dealing with the mirror universe:
- Intendant Kira Nerys' attraction to prime Kira appears to go beyond just narcissism. The show also hints at a sexual relationship with Ezri Tigan.
- Ezri Tigan later seems to hit it off with mirror Leeta.
Lastly, there was a sexy scene between Raijin and T'Pol.
For more info, see this Ex Astris Scientia article, which lists some more subtle gay/trans symbolism in Star Trek (e.g. Laas being an analogy for an openly gay character, Pa'nar Syndrome and the perceived deviance of mindmelders as an analogy for the ostracism of the gay community and the perception during the 80s of AIDS as a "gay man's disease", etc.).
No. At least not directly.
The issue of same-sex relationships was never brought forward in Star Trek. This is in all the TV shows and in the movies. The only time anything on screen came close to addressing this was in an episode of Star Trek: The Next Generation. The episode The Outcast dealt with a race (the J'naii) that had only one sex, yet there were those who identified more with one gender than another. Those who were like this and were caught were re-programmed to be "healthy" and prefer the "normal" monosexual relationships.
There was an attempt, within the 1st season, to address the topic. David Gerrold, best known for writing The Trouble with Tribbles, was a member of the writing staff at the time and wrote an episode titled Blood and Fire that featured two characters, Enterprise crewmen, who were in a same-sex relationship. The episode apparently created behind the scenes tension and it was never produced. Gerrold later re-wrote it for his Star Wolf series. After that, he re-wrote it using characters from the original Star Trek and it was produced as a two part episode as part of Star Trek: Phase II.
Not really on tv/film, but as others have said, people involved with Trek have tried to incorporate LGBTI issues and have been denied.
In the expanded universe (novels, comics, games etc) though there have been LGBTI individuals, and off the top of my head I can remember:
- Yoshi Mishima In the Starfleet Academy comic series.
- Jayme Miranda and Moll Enor from the novel TNG:The Best and the Brightest
- Burgoyne 172 and Selar in Star Trek: New Frontier
In all of these instances I recall it being pretty much a non-issue for Federation citizens.
Also here's a link to TV Legends Revealed where they talk about the previously mentioned David Gerrold's Blood and Fire episode, but there is a quote by Ron Moore, one of the writers on Star Trek, where they talk about the mindset of the time:
"We’ve just failed at it. It’s not been something we’ve successfully done. At Star Trek we used to have all these stock answers for why we didn’t do it. The truth is it was not really a priority for any of us on the staff so it wasn’t really something that was strong on anybody’s radar. And then I think there’s a certain inertia that you’re not used to writing those characters into these dramas and then you just don’t. And somebody has to decide that it’s important before you do it and I think we’re still at the place where that’s not yet a common – yeah, we have to include this and this is an important thing to include in the shows. Sci fi for whatever reason is just sort of behind the curve on all this"
Andrew Robinson provided non-canon insight into his role when interviewed by Amazon.com, stating "I started out playing Garak as someone who doesn't have a defined sexuality. He's not gay, he's not straight, it's a non-issue for him. Basically his sexuality is inclusive. But – it's Star Trek and there were a couple of things working against that. One is that Americans really are very nervous about sexual ambiguity. Also, this is a family show, they have to keep it on the 'straight and narrow', so then I backed off from it. Originally, in that very first episode, I loved the man's absolute fearlessness about presenting himself to an attractive human being. The fact that the attractive human being is a man (Bashir) doesn't make any difference to him, but that was a little too sophisticated I think. For the most part, the writers supported the character beautifully, but in that area they just made a choice they didn't want to go there, and if they don't want to go there I can't, because the writing doesn't support it."
I also vaguely recall once reading an interview with Alexander Siddig (the actor for Julian Bashir), where after being introduced to the character Garak he seriously thought that they were going to be the first gay couple on the series. Unfortunately, I cannot seem to find it now.
Roddenberry was once asked why a bald guy is commanding the Enterprise - surely by the 24th century we would have a cure for male pattern baldness? His famous answer: "By the 24th century, no one will care."
However, in the 1990s the prime-time networks were not quite ready for Brokeback Mountain in the Holodeck. In the 1960s it was really pushing the limits to put a black woman on the bridge. Note that the original first officer was female, but that didn't make it past the pilot.
So, extrapolating from 1966 (women as set dressing) to 1987 (bald men running the ship) to women captains in 1995 to girl-on-girl action shortly after, we can reasonably predict that, like baldness, by the 24th century no one will care about same-sex relationships and thus there's no need to air it today.
It was recently announced that int the upcoming Star Trek Beyond film, Sulu will have both a husband and a daughter.