It seems strange to me that one act of helping Poe escape would enable The Resistance to trust a former soldier of the First Order. He could have easily been a spy sent to gain their trust and then turned on them in the last minute to help the First Order win — like
Joe Pistone in Donnie Brasco.
After saving Poe, Finn helps Rey, but at that point she had nothing to do with The Resistance, so that really does not prove anything.
Was there another defining action or event that made The Resistance trust him?