Why didn't Atticus want the children to play their game or give Boo the note?
Atticus has always been a very fair-minded individual. He's all for giving everyone a chance, no matter what they've done or what they're alleged to have done. He's always taught his children the importance of empathy, of putting yourself in other people's shoes. And that goes for Boo Radley as much as anyone, even though he's been turned into the town's resident bogeyman by years of gossip and myth-mongering.
Atticus knows that the Boo Radley game is disrespectful; it treats him like some kind of freak; it peddles all the old myths about his being some kind of scary monster. Atticus is adamant that that's not how Boo should be regarded. He should expect to be treated the same way as everybody else. Scout and Jem wouldn't like it if they were made the object of such a game or had people leaving them strange little notes. So they should stop playing their game and leave poor old Boo alone.
It was also important to Atticus that his Maycomb neighbors in To Kill a Mockingbird live in relative peace and privacy. Atticus could see that the children's play-acting on the sidewalk was becoming a public nuisance, and he let them know that he was not happy.
"Does this by any chance have anything to do with the Radleys?"
"No sir," said Jem, reddening.
"I hope it doesn't..."
When Atticus discovered the note on the fishing line, he put his foot down. He considered Jem and Scout's unwanted intrusion as a form of "tormenting," and until then, Boo deserved the right to "stay inside free of the attentions of inquisitive children." He told them to stay away from the house until they received an invitation.
In my opinion, this is because of how Atticus disapproves of being mean to people who are weaker.
We can see throughout the book that Atticus believes you need to treat people well no matter who they are. He does not look down on the poor whites or even on the blacks who are the lowest level of Maycomb society in the book.
If he let the kids play their game or give Boo the note, he would essentially be allowing them to pick on Boo because he is such an outsider.