How comes negative norm is such a big thing for fermions that Dirac equation was chosen over KG, while the same kind of problem for photons is just ok? In fact, many books in QED do not even mention that the norm has to be indefinite to preserve covariance.
Those are two very different situations.
Dirac equation was chosen over KG only in the early days of QFT, when people haven't discovered second quantization yet. The problem was the apparent negative probability of observing a KG particle. Nowadays it is generally accepted that both KG and Dirac give consistent QFTs of particles with spins $0$ and $1/2$ respectively. All states in the 2nd-quantized theory are positive norm.
The negative norm in gauge theories is entirely different. It is a norm of a 2nd-quantized state, and cannot be given a physical interpretation. It is also not real, meaning that we don't actually get negative-norm states in the gauge theory where we have correctly accounted for the constraint equations (you don't need to justify Gupta-Bleuler by getting rid of the negative-norm states, it is just a quantum-mechanical way of imposing constraint equations. Those constraints are real, physical, exist in both classical and quantum theories and are crucial to the theory's dynamics. Negative-norm states are purely an artifact which shows up before the constraints are imposed. They don't show up in the actual theory.)