Can Robots push when moving sideways?
As you can see from page 6 of the rules:


  Pushing Other Robots
  
  When robots collide, one will push the other. Robots can be pushed
  anywhere on the board (or off the side!), even into a pit or onto a
  conveyor belt. A robot can’t be pushed through a wall, though, so the
  movement of a pushing robot will simply stop if the pushed robot runs
  into a wall. Robots can run into walls all day long without taking any
  damage from it, so they don’t accumulate Damage tokens this way.


You always push robots, unless a wall prevents them from moving. So there is no mention of direction. As long as they collide they are moved. 

This also works recursively. If robot A pushes robot B and robot B collides with robot C, then robot C is moved too (as long as there is no wall preventing movement of either robot.