Understanding Weinberg's soft-photon theorem
The universality of the coupling of the photon to charged particles exhibited by this formula is only valid in the limit of ultrasoft photons. This is also known as the eikonal approximation, in which the photon couples only to the charge x velocity of the charged particle.
Since it is valid only in the low energy limit you can think as it is the leading term of an expansion. An expression of this is that the photons with long wavelengths cannot resolve the internal structure of the source. But as you go higher energies ( next to leading order terms ) it starts to reveal the internal structure of the target.