You mean O(2), which is isomorphic to U(1). O(1) is a discrete group. You're mistaken that the existence of this U(1) is the reason that charge is conserved.

You mean O(2), which is isomorphic to U(1). O(1) is a discrete group. You're mistaken that the existence of this U(1) is the reason that charge is conserved. The U(1) you're talking about is the group of units of the complex numbers. It acts trivially in all quantum mechanical calculations, essentially because quantum mechanical states are actually rays in a Hilbert space. There is a different U(1) which is related to charge conservation. It appears in models where one can defined a charge, and acts via $e^{iq}$ on the subspace of states of charge $q$. Note that the action of this group on Hilbert space is non-trivial! It acts differently on different subspaces. In models where this group is a symmetry, by definition, time evolution doesn't alter the charge eigenstates, hence charge is conserved.