While there may be one or three who may have an issue with the QC being in charge and specifically Xavier, Erik and A, as acting "Heads of State" (which we haven't seen in-story, but it's not improbable)...I do believe the majority of mutants X-Men, New Mutants and the affiliated groups/teams are quite okies with the set up, thus far.
The X-Men teams are out and about doing X-men stuffs.
The Younger Mutants are out and about doing Young Mutants stuffs.
The "Problematic" Mutants are out and about working off some angst and misery.
The New Mutants having recently arrived on Island are busy acclimating to their new life.
No one is concerned about "Who will be nominated" in the next general elections. Or even about "How it will happen" or "When it will happen".