Anyone who says Trek isn’t horny, hasn’t watched enough Trek.

Riker has a resting 'I-want-to-fuck-the-shit-out-you' face, it doesn't matter who or what is he looking at. Chairs included.
\ And the expression only intensified when he smiles (or looks serious, or looks angry, or eats Klingon food, ... you get the idea).
Data on the other hand is very well programmed in all manner of lewdety.
And Janeway had lizard sex with a lizard. And used holodeck exactly as everyone else on the ship - for kinky romance.
Vulcans get rapey every 7 years.
Klingons have to be bitten into sexy times.
Qs had full on intercourse in front of the camera.
T'Ana is sexy in heat.
And space-life-energy thing impregnated Troi as we watched.
~~Bortus laid a fertilised~~ whoops, wrong trek.
But other than the mentioned cases, ... only many many more are not listed here.
The prime directive pretty much has a loophole clause that it doesn't apply in situations where it could become classified as a "space-genitalia-blocker".
- Goodness I love the small little Orville shout out! It was such a great intermediary before we ha Snw and LD.
  
  It really did do "some Star Trek things better than Star Trek" (I dont actually mean that literally, it's more of a product of Star Trek, of generations of fans, and geeks, and fan-geeks) ... but unfortunately the brand-name showrunner responsible for it kinda represents the worst aspects of what that future society overcame in all those centuries of advancements.
  The best number one tho.
- ~~Bortus laid a fertilised~~ whoops, wrong trek.
  He also nearly destroyed the ship with a porn virus.
  
  Ok but Im sure that one humanity will cross from the list before we leave our solar system.
  Furries in space will absolutely get into some weird stuff.
- The candle ghost episode had Picard walking in on Beverly masturbating. Getting a female orgasm on prime time TV is quite the feat.
- Bortus laid a fertilised whoops, wrong trek.
  trek at home got us through some very lean years and I will always adore it for that
  
  Indeed, it gave us substance when we needed it.

Who has ever said Star Trek isn't horny?
- There is a story about Gene coming down (to the set maybe), and wanting to check out the costumes Barbara March and Gwynyth Walsh were wearing personally. That as much as I recall. Not even sure it is a true story. Remember hearing it on Mission Log.

I just rewatched this episode and was like oh dang he really did not hold back with that kiss, even though it's dax.
Then I'm 99% sure he banged her too. Probably didn't include that in the mission brief once he got back
- I’m sure it was the hair that got Sisko.

Just watch TNG season 1 to dispel any notion of Trek not being horny.
- Dr. Barshir is explicitly a character who says they are looking for casual sex in DS9 for the first season.
  EDIT: Maybe not exactly with those words, but is always at Quarks looking for someone who will go to his quarters.

*Deep Space Nine
You meant to say Deep Space Nine.
(And all the decon scenes in Enterprise.)
- don't forget all the boning in that season 4 episode 2 of lower decks

I don't think anyone ever accused it of being prudish.
- I don’t remember which episode it was, most likely the 26th episode of All the Asians on Star Trek which Amanda Wong (background artist on LD) is interviewed. I swear someone says there was criticism over The Naked Time simulation in “I, Excretus”.

huh TIL Star Trek has scifi and political elements too
- Jfc... Next you will tell me you are surprised it deals with actual philosophical questions and actually engages the viewer in some degree of thought.