In the beginning of the series, when Offred, who is new to the Waterford station, meets fellow Handmaids at the market with her new shopping partner Ofglen, the Handmaids immediately give her advice to obtain favor with the Waterfords showing that the Handmaids try to look out for new Handmaids the best they can.
June and Moira manage to escape the reeducation centre and get to an underground station, trying to get to Boston — but while Moira, in the guise as an Aunt, is asking for which train they need to board (the signs were removed because women are not allowed to read or write), June, as a solitary Handmaid, is quickly cornered by soldiers. She nods and smiles to Moira as a sign to get on the train and escape.
After June is maimed for her escape attempt, the Handmaids at the centre each give her a piece of food they saved during lunch.
The Handmaids all gathering around a sobbing Janine after her newborn has been handed to the arms of the Wife in charge.
June and Moira's friendship. They openly say that they love each other, and clearly cling to each other for support in Gilead, even when they've been separated. Even Moira's note, which is mostly a Crowning Moment of Funny, ends with a heartwarming moment.
Praised be, bitch. — XOXO, Moira
Every time June calls Janine by her given name.
The Reveal that not only did Luke make it to Canada, he's been searching tirelessly for June and Hannah... and Moira, too. He considers June's best friend to be part of the family. Moira's so moved when she hears this, she nearly cries.
When Moira meets up with Luke in Canada, it turns out he had an alert set up if she appeared... because she's marked down as family to him, even though they're not related. This is clearly a connection she needed, since she'd been left alone in a strange land looking lost and bewildered while being inducted into the refugee center.
Moira's reasoning behind carving "AUNT LYDIA SUCKS" into a wall at the Center (well, besides the obvious), despite the penalty for being caught being losing a hand.
Moira: Once we get out of here, there's gonna be a girl that comes in here and reads it. It'll let her know she's not alone.
After Offred finds out she's pregnant and says it's terrible, Nick gently says "No it isn't", kneeling at her side as he strokes her belly, which is clearly the kind of comfort she needed in that instant.
When ordered to stone Janine to death as punishment for attempting to kill herself and her daughter, the other Handmaids are horrified and refuse to hurt her, fully aware that there'll be consequences. Furthermore, it's the Second Ofglen, the one who most wanted to stay out of trouble, who's the first to speak up for Janine.
Upon the arrest of June, Rita's first instinct is not to wonder what June has done but to give June a farewell hug, knowing that June could be going to something terrible for all she knows. This makes it clear that she valued June as a person rather than a baby vessel.
June trying to talk Janine down from attempting suicide is deeply sad, but also touching. June promises that one day, the regime will fall and then she and Janine and all the other women will all be able to go out drinking and dancing. June and Janine may have had their differences, but it's clear that in this moment, June truly empathizes with her and wants to help her believe that things will change for the better.
In a twisted way, the Wife in Ofglen/Ofsteven/Emily's new household covertly offering to fake being sick so they'd have to cancel the Ceremony that month, giving Emily a break after all the trauma she's already been through. Emily declines, pointing out she can't do that every month, but it's an odd display of genuine empathy from one of Gilead's higher-ups, showing that at least some of them have some compassion for the Handmaids.