Does symmetry violation make a approximate conservation law?

I know that Noether’s theorem relates conservation laws with symmetries, and I read that to find CPT violation, Lorentz invariance symmetry needs to be broken.
This implies that if a symmetry is broken, it’s associated conservation law becomes an approximate conservation law.
If this is the case, spontaneous symmetry breaking would have made the electric charge, color charge, and weak isospin, approximate laws, which they aren’t. This must mean that one of my assumptions is incorrect.