Pushing is usually a foul in soccer. But there’s an exception: If players are playing the ball and are shoulder-to-shoulder, they can indeed push with their shoulders to move the other player off the ball. Such “shoulder-to-shoulder” contact is allowed, even if the other player loses balance and falls.
Refs may ensure the pushing was reasonable, rather than excessive: A player can’t just ram into another player and claim shoulder-to-shoulder.
Also, the players have to be playing distance to the ball. So if two players are chasing a ball 10 yards ahead, shoulder-to-shoulder doesn’t apply until they are close enough to play the ball. And if players are playing distance but one pushes the other so far off to no longer be playing distance, a ref may call a foul. A common mistake is for a player to push shoulder-to-back (even if close to the shoulder), which is a foul.