I think the league should care about this. It is not a good look for the league to have any of this kind of thing. And if it escalates, the look gets even worse. At a minimum, if I was the "league" I would warn the Nets and I would warn Kyrie. Stop it and stop it now or I would pursue some penalties (token at first) against the Nets and against Kyrie. Probably best to pressure the team and have them deal with Kyrie but this is just stupid stuff that the league does not need.
As a fan though, I am not that upset by this. It is Kyrie who looks small or petty. I honestly am not worrying all that much about Kyrie. He came, he played, he got injured, he left, he says and does dumb things, rinse, repeat. And I am also not all that worried about whether or not some Celtics players shake his hand or hug him after games. That is just ceremony or whatever. Way to much is made of this.
As to the bottle thrower, I feel being banned from the Garden is a fair penalty. Kyrie is free to press charges if he wants but I don't think this kind of thing needs to end up in a court. Our courts really do have bigger things to be doing. A strong message was sent to the fans. This type of thing will not be tolerated. You will never come to a Celtics game again. We can move on.