The Qur'an does prohibit all marital relations with polytheists.
'Do not marry unbelieving women (idolaters), until they believe: a slave woman who believes is better than an unbelieving woman, even though she allure you. Nor marry (your girls) to unbelievers until they believe: a man slave who believes is better than an unbeliever, even though he allure you. Unbelievers do (but) beckon you to the Fire. But God beckons by His Grace to the Garden (of bliss) and forgiveness, and makes His signs clear to mankind: that they may celebrate His praise' (Qur'an 2:221)
A marriage relationship is never one which is confined to the physical plane alone. Indeed, married life finds true fulfillment of purpose only in the union of an attitude of innocent love with one of mutual respect. The Qur'an has compared the purpose of man-woman relationship with that of the clothing that one wears. '...... they are your garments and ye are their garments.' (2:187). This similitude makes clear the degree of affinity and mutuality which must exist between life-mates.
As distinct from the religions that have accepted asceticism as their ground norm, Islam views marital life as a religious obligation. In fact, Prophet Muhammad (e) had himself taught that 'he who gets married has completed one half of faith.'
The Qur'an and the practices of the Prophet have, in themselves, prescribed the exact observances that are to be maintained in marital life. It is expedient to follow these regulations even in the sexual life that is based on morality. A Muslim can, by no means, deviate from this code of conduct.
Polytheism has, of itself, no foundational basis per se. Therefore, polytheism has taken on different forms and meanings according to the variations in time and place. Similar has been the case of the rites, customs, and moral prescriptions of the polytheist. As far as the Muslim, who is obliged to follow the moral code revealed by God, is concerned he can never follow laws that have been formulated by man; particularly when such an attitude would go contrary to the tenets of the faith of his own profession. That his partner should follow a moral life that is quite contrary to his own creed, will only serve to adversely affect the religious life of the Muslim.
There are religious communities that view adultery as a religious rite. Indeed, the Hittites of Greece and the Devadasis in India, were forced into prostitution in the name of religion itself. The decree of Manu Smrithi is that if neither the virgin nor her father were to give their consent, it is permissible to carry away, by force, the woman of one's liking and then marry her. Such marriages which are permitted to the Kshathriya are referred to as Rakshasam (Manu Smrithi). It was the custom amongst the polytheists of Mecca to claim paternal rights over children who most resembled them and which where born out of extra-marital sexual relationships which they had with many wemen. Group sex was a way of salvation in many primitive religions like Tantrik religion. Undoubtedly, therefore, it would be a difficult task, indeed, for the Muslim who chooses a mate from communities of polytheists who accepted as their own such forms of moral law, to live by his own religion.
If the Qur'an had allowed the marriage with the Polytheists it would have caused much hardship for the Muslims. How would it be possible for a Muslim, to accept as his mate, a tantrik woman who practices polyandry as a religious act? It should either be that she is forced to forego her religious freedom or that he is forced to act against his religion. It would, perhaps, be also for the purpose of removing such difficulties that the Lord Creator prohibited marriages, in their totality, with the Polytheists.
The Qur'an does permit the Muslim to take mates from the 'People of the Book' who are heirs to a moral code that is as clear as it is authentic. Whether this be the Jews or the Christians, they are after all, the possessors of a religions scripture that is to ne obeyed and of a moral code that is in accordance thereof. As for this moral code, it is, at best, a rough approximation of the Islamic code itself. It is, perhaps, for this reason that the Lord Creator permitted the Muslim to marry women from amongst the 'People of the Book'.