Depending on who is or isn't showing loyalty to whom, you could make a few different arguments about what S.E. Hinton is saying about loyalty in The Outsiders. I'll put my various theme statement suggestions in italics below.
If you are thinking about Darry and Pony's loyalty to one another, you might say blood is thicker than water as a theme statement to describe how Ponyboy, Soda, and Darry all work together to be a family and stick together after their parents' deaths. You could also use Darry's decision to stay home and work full time instead of going to college as evidence of this.
At the same time, Pony questions Darry's loyalty to and love of him through most of the book. A theme statement to describe this might be when family members can't trust one another, the home dissolves into chaos. After all, it was Darry's slap that causes Pony to run away, where he and Johnny get jumped and kill the Soc. And, toward the end of the story, Soda cries out that both Pony and Darry calling on his loyalty in their arguments is tearing him apart.
Loyalty to one outside your class invites suspicion is a good theme to describe Cherry and Pony's relationship. Even though they are very similar in interests and temperament, and they get along well, Ponyboy is constantly suspicious of Cherry's motives in being his friend. At the same time, Cherry knows that being Pony's friend in a public way would be unwise, and so she keeps it private – suggesting that maybe true loyalty can't exist between social classes.