I feel like Crowley is the type of person who needs a lot reassurance. Book and TV Crowley need assurance that they are safe from Heaven and Hell, but I think TV Crowley, along with that, needs assurance that Aziraphale loves him, and accepts him and that he is worthy of love because- *voilent flashbacks from episode three*
it’s truly, reassurance seems to be a theme with the Crowleys tbh. AJ because yes, he’s got trauma from his Fall and his belief that deep down he’s one of the Bad ones and nothing can change that. coupled with Zira’s own issues, he really needs to know that he’s worthy of love and acceptance.
on the other hand, Az is more aloft than Zira and Crow has more anxiety than AJ. so even though Az and Crow are more comfortable being friends, there’s a need for Crow to prove himself. he’s a bit of a coward, i think he struggles with believing that Az won’t abandon him for whatever reason. not because he’s a demon but because of something he’s done or some way he doesn’t meet expectations.
of course demons bully Crow, i mean have you read the beginning of the book? lD at the very least, the higher up demons like Hastur don’t like him. and give his level of anxiety, i can’t imagine the “cool” façade really covers him all the time.
as for Az, i don’t think angels bully him, since Heaven is basically not involved most of the time. i think most of them are kind of morbidly fascinated by him, and don’t really know what to think of his gung-ho interests in humanity. like is he just a great angel dedicated to his job, but also why the sweaters??
for the most part, Az and Crow do their best to be in each other’s vicinities when coworkers come calling. there’s nothing like posturing as if you’re in a serious stand off to keep unwanted interactions at bay. demons show up to give Crow a hard time? sorry can’t talk right now, he’s locked in battle with the Enemy. angels asking about paperwork? sorry there’s no time to chat, he’s busy thwarting the Adversary.