I've heard different opinions about this issue, what’s the stand of Islam on a Muslim woman marrying a non-believer? What if the man claims he'd convert to Islam to be able to marry the Muslim woman? Please provide a reliable reference for each claim of yours, since I’m not interested in personal opinions.
According to jafari Fiqh:
A Muslim man is allowed to marry a Christian or a Jewish woman in temporary marriage. Based on precaution, it is obligatory to refrain from marrying a non-Muslim woman in permanent marriage. A Muslim man is not allowed to marry, neither permanently nor temporarily a non-Muslim woman who is not among Ahlul Kitab. Based on obligatory precaution, a Muslim man must refrain from marrying a Zoroastrian woman, even temporarily. As for a Muslim woman, she is not allowed to marry a non-Muslim man at all. (See the question-answer section below.)
Ref: www.sistani.org (no.390)
About claim, the parents of Girl and Girl have duty to do enough research about belief and morals of the man. There are many Hadith insisting on research about the man to have two main attributes: 1- Belief (practicing the rules of Islam) 2- Having good morals. If had this two property the marriage should be accepted according to Islam and non-Islamic terms should not be set. For example the wealth and properties of man.
A Muslim woman can not marry a non-Muslim man, no matter what his religion is. The evidence for this includes:
The following verse declares that the Kuffar (disbelievers) are not lawful husbands for them, nor they lawful wives for them. Kafir is a general term for non-muslims and Kufr includes everything that is not Islam: Judaism, Christianity, Polytheism, Atheism, Henotheism, Monaltry etc.
يا ايها الذين امنوا اذا جاءكم المومنات مهاجرات فامتحنوهن الله اعلم بايمانهن فان علمتموهن مومنات فلا ترجعوهن الى الكفار لا هن حل لهم ولا هم يحلون لهن
O you who have believed, when the believing women come to you as emigrants, examine them. Allah is most knowing as to their faith. And if you know them to be believers, then do not return them to the disbelievers; they are not lawful [wives] for them, nor are they lawful [husbands] for them.
Apart from this, marriage to Mushriqeen (polytheists) is specifically forbidden, and Shirk is in everything that denies Allah and his Oneness or sets up partners or equals with him:
ولا تنكحوا المشركين حتى يومنوا ولعبد مومن خير من مشرك ولو اعجبكم
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.
Some people have difficulty understanding how Muslim men can marry Jews and Christians while Muslim women can not. In brief the explanation is that the default rule of marriage between muslims and non-muslims is that it is forbidden, in lieu of the above two verses.
No specification or abrogation of this rule exists for the case of Muslim women, so by default they remain forbidden to marry a non-muslim husband. The case is different for Muslim men marrying a Jewish\Christian wife since an explicit exception has been made in the default rule for them in verse 5:5.
This is narrated from a group of the Sahaba, no one among them or among the tabi'in is reported to have opposed it.
جابر بن عبد الله يقول: نساء أهل الكتاب لنا حل، ونساؤنا عليهم حرام
Jabir ibn Abdullah narrated: The women of the people of the scripture are permissible for us, and our women are forbidden to them.
كتب عمر بن الخطاب: أن المسلم ينكح النصرانية، وأن النصراني لا ينكح المسلمة
Umar ibn Khatab wrote in his letter: A muslim may marry a female Christian but a Christian can not marry a Muslim female.
عن ابن عباس رضي الله عنهما قال: ... ورجالنا فوق نسائهم، ولا يكون رجالهم فوق نسائنا
Ibn Abbas narrated: ... And our men are above their women and their men are not above our women
There is Ijma' on the matter.
يحرم بالإجماع زواج المسلمة بالكافر... وعليه لا يجوز زواج الكتابي بالمسلمة، كما لا يجوز زواج الوثني والمجوسي
Marriage of a Muslim woman to a disbeliever is forbidden by consensus ... and so it is not permitted for a Kitabee to marry a Muslim woman, just like it is not permitted for an idolator or magian to marry her
There is also a lot of minor evidence which supports the view. It is a principle in Shariah that a non-Muslim can not be given wilayah over a Muslim. While in marriage a husband has guardianship over his wife. So a contract that creates such guardianship is invalid in Shariah.
ولن يجعل الله للكافرين على المؤمنين سبيلا
Never will Allah give the disbelievers over the believers a way
A non-muslim who accepts Islam becomes a Muslim in all respects, so marriage with him is permissible if his conversion was sincere.
Answer to your question is in
Surah Al-Baqarah - Aayat 221 [Chapter No. 2 Verse No. 221], as stated follows:
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.
http://quran.com/60/10 : ... And if you know them to be believers, then do not return them to the disbelievers ("alkuffar"); they are not lawful [wives] for them, nor are they lawful [husbands] for them. ... and as far as I know, Christians and Jews are accounted as disbelievers in Quran.
A brief overview
Sunni Islam Not permitted. Some communities may kaffir the women (see UmH).
Jafari Shia Islam
Civil marriage is tolerated but not accepted as a full marriage (see Battle of Karbalah).
Civil marriage is traditionally not tolerated but often tolerated in modern practise. Religious marriage is not possible.
Jewish and Christian side
Marriage with a non-Jew is not tolerated.
Civil marriage is accepted. Religious marriage is bound to educating the children as Catholics.
Civil and religious marriage is accepted by most denominations.