During the mid-22nd century, a century before Captain Kirk's five-year mission, Jonathan Archer captains the United Earth ship Enterprise during the early years of Starfleet, leading up to the Earth-Romulan War and the formation of the Federation.
This tv show contains 30 potentially triggering events.
T'Pol is 'mind-raped' in the episode Fusion and later episode Stigma uses this event as an allegory for both sexual assault and STIs, but the word 'rape' is not used and there is no sexual content.
The episode Unexpected involves Trip becoming pregnant from holding hands with a woman without knowing the risks, and the episode is largely played for laughs.
In the Risa episode, a woman (off-screen) is called "not a she" and the protagonists joke that they should have brought a scanner to verify her genitals. Another woman has her crotch leered at to verify she is "actually a she".
A Vulcan and a human have a relatiosnhip; while the actors are roughly the same age, their characters have a 30-year age gap due to Vulcans' longevity.
There are various dinner scenes between Archer, T'Pol, and Trip (sometimes between other crewmembers as well), and some people find Trip's eating sounds to be particularily noticeable.
There are no direct depictions. The show debuted on September 26, 2001, so its themes were heavily impacted by 9/11. The third season features an unprovoked attack by aliens which causes much destruction in the state of Florida. The characters then spend that season tracking down these aliens in military retaliation for the attack.
In the episode Stratagem, Captain Archer convinces Degra that the two of them are friends, that 3 years have passed since the last events of the show, etc in order to gain information from him. This makes up the entire episode. degra eventually discovers this deceit, and his memory is erased.
There's a scene in the first episode where it looks like a woman is suffocating her child with a gas mask, but T'Pol points out that she's actually trying to get her child used to breathing an oxygen-nitrogen atmosphere.
S2 E5: It is implied (but neither seen nor heard) that an alien animal's death is necessary to save the life of Porthos (the captain's dog), and obvious once we see the dog being treated as a result of that alien animal's death.
S3 E24: The Reptilians are celebrating by eating baby rats. They are picked up by their tails, and you hear their squeaks. We see them going into the mouths, but no chomping or screams of pain are heard. Still disturbing though for those who love rats.
There is a scene where prejudiced humans with an 1800s western US culture hang a "skag" as execution for being of the Skagaran race who trafficked the humans for slavery 300 years prior
There are no police, but the security teams of the enterprise could be seen as the equivalent. However, they are far more military-themed than police-like.
In the episode where the Enterprise encounters a society with three genders, a member of the third gender, clearly a non-binary individual, is frequently called "he", "her", and, most commonly, "it", with only one person correctly referring to this individual as "them".
In the season 2 episode "Cogenitor", a non-binary child commits suicide upon being refused asylum. Captain Archer claims that it was because Trip attempted to teach this child to read, and reprimands him over "causing this suicide and preventing another child from being born", but it's clear this non-binary child wasn't being asked for consent by the couple using them to reproduce, and didn't have any rights, which seems a far more likely reason than being taught to read.
In one episode, three Orion women (implied to be sex slaves) are admired both by other Orions and by Archer, Reed, etc. The entire crew is manipulated by them and the men are all sexually attracted to them.
Not in universe, but female characters (specifically T'Pol) are dressed sexually and Jolene Blalock has complained about her treatment.
There's a bunch of episodes about kids born as siblings (from eugenics) and raised as such, that end up having explicit sex scenes, fighting to decide on who has sex with whom, cheating on the other, etc.
As a bonus, they are all underage.