In the following, we will only examine the case indicated in the title. Because a Muslim man may have a wife from the followers of other Monotheistic religions, too. But let's stay with women.

Let's break this issue down into further details. First, let's examine who is Muslim according to the Quran? So, not according to Ali and Yusuf, but according to the Quran? Because, the ayas of the Quran were revealed in the life of Mohammed (peace be upon him), and the word Muslim was used in the Quran regarding prophets and their followers who lived before Mohammed, according to the original, classical sense. Submission to the One God and to be reconciled in Him. This is what the word means and it was not used to denote a religion. For the sake of completeness, I will only refer to this by indicating the numbers of ayas in the Quran: 2:132, 2:133, 2:136, 3:52, 3:64, 3:80, 3:84, 3:102, 5:111, 29:46.
According to the above verses, Abraham, Moses, Jesus and I could go on, they were all Muslims! So, Muslim means following Monotheism and not just following a single prophet! Of course, I mean the Monotheism in its original and not in a distorted form of what is present today. If we look at today's conditions, the Islam has distorted forms too, like Christianity and Judaism! (I said forms, not original teachings!). In this sense, there is no Muslim! And if we refer with the word Muslim only to shihada, the oath of creed and not to representing a value, then even a parrot can be a Muslim. First conclusion: today, the word Muslim means a religious separation on the basis of external features, ignoring the pursuit of internal values. In its original, classical form of Islam, the reverse was true: it was a unifying faith based on the inner values proclaimed by previous prophets.

Let's see the following aspect concerning Christians and Jews:

Never will the Jews or the Christians be satisfied with thee unless thou follow their form of religion. Say: "The Guidance of Allah,-that is the (only) Guidance. " Wert thou to follow their desires after the knowledge which hath reached thee, then wouldst thou find neither Protector nor helper against Allah. (Quran 2:120)

Non acceptance creates tension in the society and on individual level as well. If Jews and Christians don’t accept Muslims it makes tension but if Muslims do the same it is a mistake too. Note that this aya drives a historical allegory what Jews and Christians committed against Muslims of the age but it is linked to the phenomenon and not the subject who had committed it. At this point everybody has to cast a glance to the mirror. We all have to discover in peace that the Guidance is the one which does not make difference between us and what is for all of us.

We must place this aya in the historical context in which it was revealed. At that time, other religion meant a different political view, because a lot of interests were stuck to the religions. Or is that not the case today? After all, if we had a faith, there would be nothing wrong with us, but we became religions, so Satan broke gaps between us.
Let's continue with the forbidden category, the idolater.

Do not marry unbelieving women (idolaters), until they believe: A slave woman who believes is better than an unbelieving woman, even though she allures you. Nor marry (your girls) to unbelievers until they believe: A man slave who believes is better than an unbeliever, even though he allures you. Unbelievers do (but) beckon you to the Fire. But Allah beckons by His Grace to the Garden (of bliss) and forgiveness, and makes His Signs clear to mankind: That they may celebrate His praise. (Quran 2:221)

Marriage is the most intimate communion and the mystery of sex causes its highest fulfilment when intimate spiritual harmony is combined with the physical link. If religion is at all a real influence in life to both parties or to either party, a difference in this vital matter must affect the lives of both more profoundly than differences of birth, race, language or position in life. It is therefore only right that the parties to be married should have the same spiritual outlook. If two persons love each other their outlook in the highest things of life must be the same. Note that religion is not here a mere label of a matter of custom or birth. The two persons may have been born in different religions but if they come to see the truth in the same way, they must openly accept the same rites and the same social brotherhood. Otherwise the position will become impossible individually and socially.

Let us lay our hands on our hearts. Are we Muslims or idolaters? Don't we lick the ass of our dictators? Do we not put our prosperity, ourselves, above all other? Do we not explain Scripture according to our best interest? Are we not following people, teachers, who are manipulating us? Based on these, we can also ban ourselves from marriage with those who have faith.

Let's come to the third point. Where and when was the rule revealed what said that Muslim woman can marry only Muslim man:

O ye who believe! When there come to you believing women refugees, examine (and test) them: Allah knows best as to their Faith: if ye ascertain that they are Believers, then send them not back to the Unbelievers. They are not lawful (wives) for the Unbelievers, nor are the (Unbelievers) lawful (husbands) for them. But pay the Unbelievers what they have spent (on their dower), and there will be no blame on you if ye marry them on payment of their dower to them. But hold not to the guardianship of unbelieving women: ask for what ye have spent on their dowers, and let the (Unbelievers) ask for what they have spent (on the dowers of women who come over to you). Such is the command of Allah. He judges (with justice) between you. And Allah is Full of Knowledge and Wisdom. (Quran 60:10)

Under the treaty of Hudaybiyah women under guardianship (including married women), who fled from the Quraish in Makkah to the Prophet's protection at Madinah were to be sent back. But before this Ayah was issued, the Quraish had already broken the treaty, and some instruction was necessary as to what the Madinah Muslims should do in those circumstances. Muslim women married to Pagan husbands in Makkah were oppressed for their Faith, and some of them came to Madinah as refugees. After this, they were not to be returned to the custody of their Pagan husbands at Makkah, as the marriage of believing women with non-Muslims was held to be dissolved if the husbands did not accept Islam. But in order to give no suspicion to the Pagans that they were badly treated as they lost the dower they had given on marriage, that dower was to be repaid to the husbands. Thus, helpless women refugees were to be protected at the cost of the Muslims.
A non-Muslim woman, in order to escape from her lawful guardians in Makkah, might pretend that she was a Muslim. The true state of her mind and heart would be known to Allah alone. But if the Muslims, on an examination of the woman, found that she professed Islam, she was to have protection.

So, the rule was linked to a historical context.

And now come to the fourth aspect. At that time, Muslim men were men of inner values and women were women of inner values. They replaced the era of Jahiliya, that is, ignorance, barbarism, and spread morality, legitimacy and pure faith. The Quranic revelations were applied to them and not to the today Arabic and other Muslim caricatures with soft spine. These today have nothing to do with revelation in terms of value, just in terms of words.

Based on the above, I will ask you back. Who do you choose? The who carries the values of Islam, or who repeats stereotypically something while committing the greatest sins that can be committed, all referring to Allah? Take a decision.