What was the argument about?
Argument was about Yandu breaking the Ravagers code in past. Here is the full conversation:
Yondu: Are you gonna listen to what I got to say?
Stakar Ogord: I don't got to listen to nothing, you betrayed the code! > Ravagers don't deal in kids!
Yondu: I told you before, I didn't know what was going on!
Stakar Ogord: You didn't know, because you didn't want to know, because it made you rich! - IMDb
Why was Yondu outcast?
For the same reason, "breaking the Ravagers code". Yando was stealing Ego's kids for him and Peter was one of those kids too which he didn't delivered to Ego. Here is a related question to that.
Was there anything from the first movie that ties into this that I should be remembering?
Not much, Stakar Ogord's character appeared for the first time and Ravager's code and other Ravagers came in MCU for the first time. But Yando did mentioned about not delivering Peter in first film:
Kraglin: Yeah, Quill turned out okay. It's probably good we didn't deliver him to his dad like we was hired to do.
Yondu Udonta: Yeah, that guy was a jackass. src
Note: Stakar is a important character form Marvel comics and might play important role in future.