Saying that a photon travels on a geodesic means a geodesic of spacetime. Spacetime is four dimensional without any particular prefered 3D+T slicing, so you cannot simply translate this geodesic to particular spatial directions.But a straight path implies direction towards something. What is the photon travelling towards? Or, what is causing photons to move in a straight path?
In 3D space, e.g. how an observer sees the world around him, the path light does not always appear to be a straight line. This is for instance the case when a light path comes near an object of mass. Gravity influences how we observe those paths. Similarly we can observer that a radar signal takes longer when the path between two objects is influenced by gravity. In extreme cases we never even get the return signal from the radar signal we sent.