Its better to undertand the principle from following video
https://www.youtube.com/watch?v=gFnPPw5ccXI

From above video, you can understand that before marriage what you have to consider if religion matters to you.

For a person who is laready married and become muslim then what Qari sab has said is right.

It is true that immediate addresses of these verses were Polytheists of Arab. But Quran did not stop there, in-between describing menace of Polytheism (shirk), Quran has also given statements with universal applicability e.g.

“And wed not idolatrous women, unless they embrace faith, and [remember] a believing slave-girl is better than an idolatrous woman, although you may fancy her. And wed not your women to the Idolaters, unless they embrace faith. And [remember] a believing slave is better than an idolater, although you may fancy him” (2:221)

Other than this, Quran also equated a culprit of fornication with that of a polytheist as being these two only eligible for getting married to each other. Here also, sentence structure doesn’t demand specific application only. [1]

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[1]

…”The second requisite of marriage stated in the verse is chastity. No adulterer has the right to marry a chaste woman and no adulteress has the right to marry a chaste man, except if the matter has not gone to court and the two purify themselves of this sin by sincere repentance. The words مُحْصِنِينَ غَيْرَ مُسَافِحِينَ point to this pre-requisite. At another place, the Quran says:

الزَّانِيلَا يَنكِحُ إلَّا زَانِيَةً أَوْ مُشْرِكَةً وَالزَّانِيَةُ لَا يَنكِحُهَا إِلَّا زَانٍ أَوْ مُشْرِكٌ وَحُرِّمَ ذَلِكَ عَلَى الْمُؤْمِنِينَ (3:24)

The man guilty of fornication may only marry a woman similarly guilty or an idolatress and the woman guilty of fornication may only marry such a man or an idolater. The believers are forbidden such marriages. (24:3)

It is obvious from this verse and also evident from divine scriptures that fornication and polytheism are exactly similar to one another. Just as it cannot be acceptable in any way that a husband or wife commit marital unfaithfulness, similarly, it is totally unacceptable for a Muslim that someone else besides the Almighty be worshipped in his house. In fact, this is more detestable a sin than sleeping with some other woman. This similarity between fornication and polytheism could have been deduced; however, the following Quranic verse explicitly states it:

وَلَا تَنكِحُوا الْمُشْرِكَاتِ حَتَّى يُؤْمِنَّ وَلَأَمَةٌ مُؤْمِنَةٌ خَيْرٌ مِنْ مُشْرِكَةٍ وَلَوْأَعْجَبَتْكُمْ وَلَا تُنكِحُوا الْمُشْرِكِينَ حَتَّىيُؤْمِنُوا وَلَعَبْدٌ مُؤْمِنٌ خَيْرٌ مِنْ مُشْرِكٍ وَلَوْ أَعْجَبَكُمْ (221:2)

And wed not idolatrous women, unless they embrace faith, and [remember] a believing slave-girl is better than an idolatrous woman, although you may fancy her. And wed not your women to the Idolaters, unless they embrace faith. And [remember] a believing slave is better than an idolater, although you may fancy him. (2:221)

The Jews and Christians of the Prophet’s times were also deeply incriminated with the filth of polytheism both in their beliefs and in their deeds. However, since they were basically monotheists, the Almighty was lenient enough to Muslims to allow marriage with their chaste women:

وَالْمُحْصَنَاتُ مِنْ الَّذِينَ أُوتُوا الْكِتَابَ مِنْ قَبْلِكُمْ إِذَا آتَيْتُمُوهُنَّ أُجُورَهُنَّ مُحْصِنِينَ غَيْرَ مُسَافِحِينَ وَلَا مُتَّخِذِي أَخْدَانٍ (5:5)

And [lawful to you in marriage] are also chaste women from among these People of the Book before you when you give them their dowers with the condition that you desire chastity not lewdness nor becoming secret paramours. (5:5)

It is evident from the context of the above verse that this permission was granted when no confusion remained regarding tawhid(monotheism) and it prevailed over the polytheistic Arab society in every manner. It should be kept in mind that the verse quoted above begins with the word اَلْيَوْم (this day). This word shows that the permission given was also very much dependent on the circumstances of those times: It was expected that if Muslim men would marry among the People of the Book these women would be positively influenced by Islam. In this way, not only would there be no clash between monotheism and polytheism, but also there was a great chance that most of them would accept Islam.

Consequently, Muslims today must necessarily take this aspect into consideration if they want to benefit from this permission.“…

(Excerpt from Meezan: Javed Ahmed Ghamidi)

(Translated by Dr. Shehzad Saleem)

For complete article, please see:

Discussion 29887

For detailed comments of Ghamidi Sahab on Intersect and Interfaith marriages, please refer to the following threads:

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@UmerQureshi
what about partners of converted muslims?

There is no obligation to break off ties of Nikah. It depends on reverted person’s own preference, whether he/she wants to carry with that Nikah or not. Prophet Muhammad (sws) broke Nikah of marriages of Muslims (including his daughter) with Polytheists at a very later stage after Itmam-e-hujjat was done on those Polytheists. This was done in tandem with other measures taken to break off all ties with polytheists including inheritance ties and others, but only after Itmam-e-Hujjat..

Please also refer to the video below from 4:12 to 4:59

https://youtu.be/3kfdJeY-9As?t=252