Gravity can affect light. If gravity didn't affect light, it would be possible to violate the conservation of energy.
A high energy photon can turn into an electron/positron pair. A massless particle can convert into massive particles. Imagine I got really good at managing the back-and-forth transition between high energy photons and electron/positron pairs. Enough that I could control it with very high efficiency and control. (Unlikely, but we're talking physics violations here. Assuming difficult engineering is fine.)
So let's say I'm really good at converting back and forth between photons and electron/positron pairs. Good enough that I can build a machine that can do this in bulk with high efficiency. (We'll also assume mirrors of unreasonable reflective efficiency.)
If gravity did not affect light, I could use such a conversion machine as a free energy device.
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Convert into photons and store in a mirrored box.
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Lift the mirorred box to a great height.
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Once at a height, convert the photons back to electrons/positrons.
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Lower the box down, using the falling weight to spin an electric generator.
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Once on the ground, convert back to photons and repeat.
Conservation of energy demands that gravity be able to affect light.