Since Einstein, we know gravity is the curvature of space-time. It may be represented as a force in calculations but in reality there is no force.
How about I turn that around and say that Einstein showed gravity can be modelled by the curvature of space-time but in reality it is a force? The fact of the matter is that, at a fundamental level, we have no clue what gravity is. However you can represent it very well by a spin-2, mass-less particle which couples to a particle's 4-momentum (the caveat being that you cannot make this theory work without an energy cut-off at some scale for which there is no justification). Until we solve quantum gravity we simply do not know what gravity really is but, if I were to bet, I suspect the latter is closer to the truth but needs some correction for the quantum structure of space-time which is something we have no clue about.
If gravity is not a force then do we really have a hierarchy problem?
Yes, and if anything it would be worse. The current problem comes about because we cannot scale the Higgs corrections up to the Planck-scale where we know there is new physics. If we remove that scale then we have a theory which has no upper scale limit and so should generate infinitely large corrections to the Higgs mass i.e. we go from an incredibly unlikely 1 in ~10^34 chance of the corrections giving such a light Higgs to a zero percent chance of the theory giving a light Higgs, or any Higgs with a non-infinite mass.
Obviously, if this is the case, G has nothing to do with Fermi's constant and we should not compare the two.
You are getting your 'g's and 'G's confused. In the muon g-2 experiment the 'g' is the muon's anomalous magnetic dipole moment. This is a precision test of Quantum Electrodynamics. The high order corrections to this will involve Fermi's constant (G_F) due to W and Z loops but these contributions will be incredibly small and were this any other experiment I would have said negligible but perhaps not in this case given the incredibly high precision involved. Neither of these constants have anything to do with the gravitational constant (G) nor the local acceleration due to gravity (g). So we are not comparing the two.