All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
In principle divorce is allowed, it many be desirable, obligatory, disliked or forbidden according to different situations. So if the wife is as mentioned in the question, then she is wrong and committed great sins. She is considered a disobedient wife, so her husband should follow the steps set by the Islamic Law when dealing with a disobedient wife; this is clarified in Fatwa 89480, so please refer to it.
If she then repents and becomes righteous, all perfect praise be to Allaah, otherwise it is desirable for him to divorce her as it is no good for him to keep such a bad woman.
So it is desirable to divorce her if she supplicates the dead in the graves, or pious people, or if she does not believe in Allaah's Might, but not to the point that takes her out of the fold of Islam. If her belief takes her out of the fold of Islam, like calling upon dead [or live] pious people, or seeking their help and the like, then it is forbidden for him to keep her and it would be an obligation on him to divorce her as long as she believes in this.
Finally, it should be noted that a person who wants to marry, should choose a religious woman with a good moral conduct, and he should be keen on teaching them the matters pertaining to their religion especially the principles of belief.
Allaah Knows best.