A Muslim woman's marriage to a non-Muslim man is prohibited according to scholarly consensus
7-8-2014 | IslamWeb
Question:
Assallamu Allaikum.. I'm a reverted muslimah who is being with non parents to make them understand Islam. However I say they are refusing it and looking a non-Muslim guy for me. recently i came to know about Zynab(RA) marriege. I read out this "Zainab (R.A.) was the eldest daughter of the Prophet (PBUH) and was born in the fifth year of his marriage to Khadijah (R.A.), when he was thirty years of age. She embraced Islam and was married to her cousin Abdul-As-bin Rabi. Her husband fought in 'Badr' for the Qureysh and fell a captive to the Muslims. Her husband also embraced Islam later and joined her in Madinah." so as per this our prophet accepted his daughter to marry a non muslim. Mohammad(SAW) is our role model and we get sunnah by following him so even we can do that?
Answer:
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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Firstly, we congratulate you for embracing Islam. Verily, Islam is the true religion of Allaah by which He has abrogated all the previous divine Messages. Therefore, Allaah does not accept any other religion from His slaves. We implore Allaah to bless you and us with steadfastness on the path of Truth until death so as to achieve Paradise and savor the eternal bliss and everlasting happiness therein. We advise you to keenly seek beneficial knowledge, carry out good deeds, and attend religious lessons and gatherings in Islamic centers and other places.
You have done well by keenly striving to guide your parents to the Straight Path and invite them to embrace Islam. We supplicate Allaah to render you a cause for their guidance. The Prophet, sallallaahu ‘alayhi wa sallam, said: “It will be better for you that Allaah should give guidance to one man through you than that you should acquire the red ones among the camels (i.e. high breed camels).” [Al-Bukhari and Muslim] We advise you to supplicate Allaah for them and to show them the merits and virtues of Islam through your conduct and dutifulness towards them.
As for your question about marriage, it is impermissible for a Muslim woman to marry a non-Muslim man; this is a well-established rule according to scholarly consensus as underlined in Fataawa 84265 and 89770. One of the rationales for this – other than compliance with the command of Allaah – is that a woman tends to be overwhelmed by her emotions. So, it is feared that her marriage to a non-Muslim man would negatively affect her and lure her into disbelief, as some scholars highlighted.
As for your remark about the story of Zaynab 
the daughter of the Prophet, sallallaahu ‘alayhi wa sallam, and her marriage to Abu Al-‘Aas ibn Ar-Rabee‘, it should be noted that they got married in the Jaahiliyyah (pre-Islamic era). After her conversion to Islam, Zaynab migrated to Madeenah and their marriage (to her non-Muslim husband) came to a halt until he embraced Islam later on. After his conversion to Islam, the Prophet, sallallaahu ‘alayhi wa sallam, approved resuming their marriage with their first marriage agreement (with no new marriage contract). This story has nothing to do with the Muslim woman’s marriage to non-Muslim man. Please refer to Fatwa 129788.
Finally, you should try to kindly convince your parents that Islam does not approve such a marriage and it is considered Zina and a hideous and disgraceful act. In the meantime, you are advised to seek the help of your fellow Muslims to find a pious Muslim man who is a suitable spouse for you in order to put an end to this problem. It should be noted that it is permissible for a Muslim woman to ask a righteous man whom she wishes to marry to be her husband as long as this is done within the limits and boundaries of noble Islamic manners set by the Sharee‘ah. This has been highlighted in Fatwa 82471.
Allaah Knows best.