I claim that relative configuration spaces are standard examples of abstract configuration spaces in undergraduate physics classes. I'm not sure where it falls in the curriculum, but Noether's theorem is known to all physicists. I'm not sure exactly how they phrase that theorem, but symplectic reduction is a version that says that there's a general procedure for producing relative configuration spaces from symmetries.

Maybe I'm overstating these generalities, but I think the claim that relative configuration spaces are unknown to most physicists is absurd.