In Einstein's general relativity, GR, the old familiar parameters don't have the same meanings as those of classical physics. I believe this is a subtle result of the redefinition of space and time. Consequently, it is claimed that light has no mass, as mass is defined in GR. The concept of force is absent from GR. I am not comfortable applying GR, so I cannot dispute those claims. Instead, I shall demonstrate that, in classical physics, it is entirely consistent to attribute mass to a photon.

For a particle with rest mass, at non-relativistic speeds, force is defined by the formula, f = ma. Turning that around to m = f/a serves as a definition of mass. However, those formulas are not valid at relativistic speeds because it takes greater force to account for the increasing mass. A better definition of force is f = dp/dt, the rate of changing momentum, which is valid at all speeds. That formula is even valid for a photon at the speed of light.

A photon's momentum does change in response to gravity, so it does feel a gravitational force of attraction. To preserve the principal of conservation of momentum, it must be true that the mass which attracts the photon is also attracted to the photon. Thus, a photon has gravitational mass.

For particles with rest mass at relativistic speeds, dp = mdv + vdm, so f = d/dt(mdv + vdm), where m is the rest total mass, including relativistic mass.

For a photon, f = dp/dt = d/dt(E/c) = d/dt(mc), where m is the mass equivalent of E, as in E = mc^2. So a photon has inertial mass.

QED