Leia wasn't the only one not liking the shooting of these people. While the demons deserved as many bullets as possible, the bodies they were possessing didn't. They were innocent people. But the last thing River and Leia needed were to not take the strategic shots and get themselves impaled on something or knocked out. Or worse. So River would take the shots as they came, and then get the people to a hospital later, provided the people weren't dead when the demons possessed them.
River gritted her teeth as Leia was flung into the planks. All right, that was it. She was done playing. She spouted the next couple lines of the exorcism, taking advantage of the little lull in battle. Thankfully, speaking the words caused the demons to stop their attack and focus more on trying to resist. Though it wasn't really working as the black smoke started to come out of their mouths as the demons choked and felt themselves being pushed back to Hell.
River kept her gun pointed at them in case they renewed their attack.