What are some things Atticus says in the novel, To Kill a Mockingbird, that represent acceptance? Some things that show he knows he is going to...

You basically ask three questions - how does Atticus show acceptance, where does Atticus show understanding that he will lose the case, and where he believes in equal rights. 

First, Atticus's whole life shows acceptance. Let me give you a few examples. He treats Calpurnia, a black woman, with respect and courtesy.  In fact, she is very much a part of the family.  The black community loves and respects him.  This is only because they...

You basically ask three questions - how does Atticus show acceptance, where does Atticus show understanding that he will lose the case, and where he believes in equal rights. 

First, Atticus's whole life shows acceptance. Let me give you a few examples. He treats Calpurnia, a black woman, with respect and courtesy.  In fact, she is very much a part of the family.  The black community loves and respects him.  This is only because they know him to be an honest and good man towards all. Finally, he also shows acceptance to people like the Cunninghams. He does legal work for them, even if they cannot pay with money. 

Second, Atticus is a realist. He knows the racism of Maycomb. He knows that he will lose the case.  He actually says this. Here is the quote:

“Atticus, are we going to win it?"

“No, honey."

“Then why—"

“Simply because we were licked a hundred years before we started is no reason for us not to try to win,” Atticus said.

Finally, as for equal rights, the case with Tom Robinson shows Atticus's strong belief in equal rights.  He defends him at all cost. In other words, he goes into the fray with his eyes wide open, knowing that hardships will come.  That speaks volumes.