The entire fandom would benefit from rewatching season 1 because i feel like far too many people are suffering from only remembering the fanworks disease.
Aziraphale kept information from Crowley and reported to heaven. It took him a long long time to finally take it into his own hands and do something to prevent the apocalypse. It took him until he spoke to Mettatron and got discorporated.
The bandstand scene's conflict is almost the same as what they argue about at the end of season 2. "Let's run away" vs. "No, I can still change heaven's mind"
No one is out of character, it's just that they haven't been given a good enough reason to realise these mindsets are harmful.
Maybe Aziraphale knows they wanted to execute him, maybe he knows how Gabriel was acting, but he's far too forgiving, far too willing to let bygones be bygones if it means the worldview he's supposed to believe (that heaven is inherently good) remains unchallanged.
And Crowley is still trying to run. He wanted to just kill the antichirst and be over with it, he wanted to run away from the apocalypse to alpha centauri, and he had no interest in being around Gabriel in season 2 because it threathened the "fragile existance he's carved out for himself." At the end he proposes going away again. He's avoidant, he's nervous. If you just put sunglasses over it it's like the serpent eyes were never there in the first place.