The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers. (Qur'an 24:3)
And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember. (Qur'an 2:221)
The above verses explain concerning polytheists.
And a possible definition of a believer which describe the eligibility for a woman to be called as a believer.
Muawiya ibn al-Hakam came to the Prophet (Allah bless him and give him peace) and told him, "I am very newly from the Jahiliyya, and now Allah has brought Islam," and he proceeded to ask about various Jahiliyya practices, until at last he said that he had slapped his slave girl, and asked if he should free her, as was obligatory if she was a believer. The Prophet (Allah bless him and give him peace) requested that she be brought, and then asked her, "Where is Allah?" and she said, "In the sky (Fi al-sama)"; whereupon he asked her, "Who am I?" and she said, "You are the Messenger of Allah"; at which he said, Free her, "for she is a believer" (Sahih Muslim).
And now what about those other religions in which people worship although only one God, but to some Monkey God or Moon God, then it is most likely that, that woman of that religion wouldn't believe that Prophet Muhammad (pbuh) is a messenger of God, but, still to answer and to be more accurate, ask her "Who created that Monkey God or Moon God", if she answers, that Monkey God or Moon God existed all by itself, then leave her, else if on reminding her that there is 'something which created everything including that Monkey God or Moon God', and if she recognizes, realizes and affirms to that fact, along with believing that Prophet Muhammad (pbuh) is the messenger of that 'something which created everything', then you can marry her.
So in short, a Muslim man is allowed to marry a 'non-Muslim (and non-Ahl-al-Kitab) woman' only if she believes according to the definition fore mentioned. Prior to becoming a believer, no one cannot marry her while she is unbeliever.
No matter what the school of thought is, everyone abides by the verse 2:221 i.e. a verse from Qur'an if he has to be called himself as a believer because this is ruling is from Allah. As far as I know there must not be any disparity in this issue.
May the creator guide us all.