It appears that the accepted answer is that photons do not have mass and gravity does not affect photons; instead, gravity warps space-time causing a change in what the straight line is, the path of least resistance, which causes the change in direction.
If this is true, then everything works out as long as you accept this distortion was not proved or accepted at the time.
If this was an unknown phenomenon, discovered when starlight was observed passing an eclipsed sun to show light changes direction due to the sun’s gravity warping time and space. there would have had forces that were not accounted for in classical Newtonian physics. Instead they used this new phenomenon to account for the change in direction of the massless photon.
This seems a bit disingenuous, where is the missing affect that this warped time space would have had on objects that have mass. If they had the instruments good enough to measure the change of the starlight around the sun, their measurements would have showed that there was missing force on objects with mass before the discovery?
To think that science has answered all the questions correctly at this point in history is unrealistic. For example science has no clue about how gravity works. It has no idea about what the size of the Universe is. The Big Bang has so many holes in it you could shove galaxies through them. It also seems that current scientists have misinterpreted what Einstein said about certain parts of his theory of relativity.
If you have the chance, I encourage you to read what Einstein said about relativity in layman terms. ‘Evolution of Physics’ by Albert Einstein and Leopold Infeld, it is very educational.
Here are some links to the current theory of mass changing space time to produce a change in direction of the massless photon:
Science is always discovering odd scraps of magical wisdom and making a tremendous fuss about its cleverness. ~ Aleister Crowley
We keep, in science, getting a more and more sophisticated view of our essential ignorance. ~ Warren Weaver