As this is a Heartwarming Moments page, spoilers will be left unmarked. You Have Been Warned!
The entire concept behind City 31. Humanity has just fought off an alien occupation that lasted for 20 years, and not only did it find it within itself to not immediately go Absolute Xenophobe on the invaders, but five years later, City 31 stands as a tribute to just what cooperation can get you. Yes, the transition hasn't been smooth, but humans are no longer alone in the universe, and it is clearly for the better.
The dynamic between the teammembers, regardless of species. You get the feeling that these people have been working together for a while - long enough to develop their own friendships and (often snarky) humor.
Godmother and Claymore are the parental figures of the whole team, keeping things orderly and supporting the newcomers with any difficulties they face.
Axiom actively tries his best to keep his anger management issues from spoiling things, and sometimes joins in conversations, willing to share his experiences.
Verge also shares his wealth of experiences, and is willing to pay for people's meals so he can enjoy the taste via proxy.
Cherub is an endless fountain of good cheer, and he brings the others together with his encouragements.
Torque has issues dealing with noncombat/social situations, but she still tries hard to fit in (with encouragement from Jane Kelly), and even finds time to sketch all sorts of things, including Axiom while he enjoys ramen.
Patchwork does her best to remind the others that technology can do great things, as she still has good memories of the time ADVENT made prosthetics for her.
Practically everything about Jane Kelly. By canon, she fought through the entirety of XCOM 2, facing down the horrors of the alien war machine and getting a front-row seat to the nightmare that was the Avatar Project. She would be well within her rights to be screaming for every single alien's head on a pike, but instead, she chose to become an advocate for alien life coexisting with humanity, going so far as to form the Reclamation Agency and personally oversee Chimera Squad. In a world where things are held together by the flimsiest of threads, it's nice to see a true pillar of light in the darkness that is the post-war world of XCOM.
In its own strange way, the motivations behind the Gray Phoenix. They're not out to restore the fallen ADVENT order or enact purges against anyone who isn't one of them, all they want is to find a way to go back home. Spirals into tearjerker when one considers that they, like the Elders before them, could have simply gone to humanity to ask for help with their problems, and avoided all the senseless bloodshed that followed.
On the same note, doing Grey Phoenix first while spamming tranq rounds results in the one antagonist group that is well-intentioned walking away minus some dignity and resources but alive and probably not that badly off.
A set of Viper-centric posters celebrating personal egg incubators cumulates with a crayon drawing by a baby Viper with the words "I love you mom" written on it in sprawling black crayon. In several of the locations Chimera Squad can visit, you can find bunk rooms with a heated rock and an incubator set aside for a Viper roommate. There's also a poster of a human and a viper working together in the medical business.
Several posters encourage the other races to keep and care for pets, like cats.
One poster depicts a lady and a muton in a suit enjoying a drink together.
Mutons are shown in various posters encouraging their brethren to adopt Earth's fashion, farming crops, raising families (with muton children depicted alongside their parents), and generally enjoying a life at peace.
What appears to be a pair of Faceless enjoying coffee together, with the words "Coffee Brings Friends Together"
Civilians on a mission can be of most races present in the city. When it's one of the races bred for combat, like a Viper, they're hunkered down in a much more defensive pose... but still wait in place to be rescued like a more fearful human or sectoid. They're civilized enough they'd rather wait for a chance to get out than shed blood randomly.
Archons (and Floaters) are revealed in a background detail to have been given a psionic refuge to rest their minds after their long torment by the Elders. It is even noted that without the horrible agony of their cyborg state afflicting them, they are at peace. Verge in particular empathises with their fate (Being most familiar with them due to his former life as a Sectoid Commander from the first invasion and thus having spent a lot of time near Floaters and then Archons that were in constant agony), and is the agent most willing to ensure that all remaining Archon Control Collars he knows about are confiscated by the Reclamation Agency and disposed of, so no other Archon needs to suffer.
During one mission, you find a captured and terrified Archon the Progeny are trying to brainwash. Everybody on your team, even Godmother and Torque become utterly zealous in stopping that.
Godmother: "This creature goes home today. You hear me?"
Background text reveals that Mayor Nightingale, while ruthless in confiscating restricted weapons from smugglers, was quite willing to legitimize smugglers that were merely sharing food supplies with refugees both within and without the city, as she was one of them once during the brief time she was purposeless after ADVENT was defeated by XCOM and the Resistance.
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