I definitely don't think the Robins were outcasts. But what friends did Tim have before meeting Batman. I know we met his public school friends in the 90s (I liked them existing), but I don't recall meeting or hearing reference to any school friends before he moved to Bristol (honestly, I'm not sure where his parents lived before that - they were later said to have a penthouse in Gotham and Tim himself was in boarding school at the time we met him). Did we meet them later or see them in flashbacks? Anyway, I don't remember anything indicating him in a outcast state, certainly. But I also certainly don't remember everything.Tim and Dick cannot be described as outcasts by any definition of the word. Dick was taken in because Bruce felt sorry for him after his parents died and Tim was a suburban-raised kid who had his own circle of friends before he ever met Batman. Damian isn't an outcast just anti-social and Duke also had friends before he met Bruce.
For me, an outcast is someone who isn't accepted or welcome in the larger society around them (could be school, community, or general world). Definitely applies to the Doom Patrol. Doesn't really apply to any of the Bats who immediately come to mind. Tim had a bully at his first school, sure, but plenty of friends, and the entire group was not generally ostracized. Dick has always been generally well-liked. Barbara and Steph and Duke are all ones who seemed to have friends, even if we didn't see them much. Cass and Jason might come closest in the sense of how the homeless are generally treated. Cass's communication difficulties separate her from people, but not equate to outcast status to me. Alfred and Bruce are easily accepted in larger society and both used to have friends before Bruce got all brooding (and who they think he is is still very accepted) and before Alfred became all about Bruce. Damian's a weird case. Can't really comment on everyone else.