It has nothing to do with the belief in God.
One can be a Hindu and remain an Atheist ,like Carvakas, Buddhist,Ajivaka.
These are totally opposed to Vedas and deny their authority.
Orthodox systems are those which belive in the Authoroty of the Vedas.
Those, like Jainism are called Heterodox and they do not believe in the Vedas.
Even among the Orthodox systems which believe in the authority of the Vedas deny God, like The Nyaya System.