Photons have no rest mass, but one of the key points in GR is that mass and energy are interchangeable by E=mc^2. Mass-energy equivalence is how Fission bombs work.
Photons have no mass, period. An ensemble of photons may have a non-zero invariant mass, but there's just no way in which it's correct to say a photon has a mass.
This has nothing to do with saying that you can't convert mass to energy. Electron-positron pair creation from ultra high energy gamma rays has been a known thing for a long time. Pulsars are thought to run partly off of pair creation off the magnetic field, etc.