How does Newton's third law apply to baseball?
When you hit the ball with the bat, the ball hits you with the bat. (At least in terms of forces)
According to Newton's third law, the force exerted by the bat hitting the ball will be equal in magnitude but opposite in direction of the force the ball exerts on the bat.
Generally, your arms are stiff when you hit the ball forward, so you will not feel the bat "recoiling". But if you relax your arms you will feel the bat being "shot" backward the moment directly after you hit the baseball- all according to Newton's third law.