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A Summary of Subsidiary Injunctions
1. We know from the initial verses that the case brought to the Holy Prophet (SM) by the Jews was decided by him. The decision was in accord with the Shari'ah of the Torah. This proves that the religious injunctions in force in the previous Shari'ahs remain in force until abrogated by the Holy Qur'an or Divine Revelation as it was in the cases of the Jews where the injunction concerning equality in Qisas (Law of Retaliation) and stoning to death (Rajm) in punishment of adultery (Zina) was there in the Torah as well. Then, the Qur'an too retained it as it was.
2. Similarly, in the second verse (45), the injunction of Qisas about the Retaliation for Wounds which has been mentioned with reference to the Torah was enforced in Islam by the Holy Prophet (SM). On this basis, the rule of procedure with the majority of the 'Ulama of Islam is that injunctions of previous Shari'ahs which have not been abrogated by the Qur'an are valid, enforcable and obedience-worthy in our Shari'ah too. That is why, in the cited verses, the people of the Torah have been asked to decide, judge and obey in accordance with the Torah and the people of the Injil have been asked to decide, judge and obey in accordance with the Injil though both these Books and their Shari'ahs stand abrogated after the appearance of the Holy Prophet (SM). The outcome is that the injunctions of the Torah and Injil which were not abrogated by the Qur'an are obedience-worthy even today.
3. The third injunction which stands proved from these verses is that ruling contrary to the injunctions revealed by Almighty Allah is Kufr (disbelief in and rejection of Faith) under some conditions specially when it is combined with belief in its being not true. And under some conditions, it is Zulm (injustice) and Fisq (disobedience, sin) when belief-wise, one does accept them as true, but, in practice, does what is contrary to it.
4. The fourth injunction which appears in these verses is that taking bribe is absolutely Haram (unlawful)- specially, the taking of bribe in a judicial case, which is far too grave.
5. The fifth injunction which emerges clearly from these verses is that all prophets, may peace be upon them, and their Shari'ahs agree in principle, but there is that difference in minute and subsidiary injunctions with them - a difference which is based on considerations of great wisdom.
Verses 51 - 58
يَا أَيُّهَا الَّذِينَ آمَنُوا لَا تَتَّخِذُوا الْيَهُودَ وَالنَّصَارَىٰ أَوْلِيَاءَ ۘ بَعْضُهُمْ أَوْلِيَاءُ بَعْضٍ ۚ وَمَن يَتَوَلَّهُم مِّنكُمْ فَإِنَّهُ مِنْهُمْ ۗ إِنَّ اللَّهَ لَا يَهْدِي الْقَوْمَ الظَّالِمِينَ
فَتَرَى الَّذِينَ فِي قُلُوبِهِم مَّرَضٌ يُسَارِعُونَ فِيهِمْ يَقُولُونَ نَخْشَىٰ أَن تُصِيبَنَا دَائِرَةٌ ۚ فَعَسَى اللَّهُ أَن يَأْتِيَ بِالْفَتْحِ أَوْ أَمْرٍ مِّنْ عِندِهِ فَيُصْبِحُوا عَلَىٰ مَا أَسَرُّوا فِي أَنفُسِهِمْ نَادِمِينَ
وَيَقُولُ الَّذِينَ آمَنُوا أَهَـٰؤُلَاءِ الَّذِينَ أَقْسَمُوا بِاللَّهِ جَهْدَ أَيْمَانِهِمْ ۙ إِنَّهُمْ لَمَعَكُمْ ۚ حَبِطَتْ أَعْمَالُهُمْ فَأَصْبَحُوا خَاسِرِينَ
يَا أَيُّهَا الَّذِينَ آمَنُوا مَن يَرْتَدَّ مِنكُمْ عَن دِينِهِ فَسَوْفَ يَأْتِي اللَّهُ بِقَوْمٍ يُحِبُّهُمْ وَيُحِبُّونَهُ أَذِلَّةٍ عَلَى الْمُؤْمِنِينَ أَعِزَّةٍ عَلَى الْكَافِرِينَ يُجَاهِدُونَ فِي سَبِيلِ اللَّهِ وَلَا يَخَافُونَ لَوْمَةَ لَائِمٍ ۚ ذَٰلِكَ فَضْلُ اللَّهِ يُؤْتِيهِ مَن يَشَاءُ ۚ وَاللَّهُ وَاسِعٌ عَلِيمٌ
إِنَّمَا وَلِيُّكُمُ اللَّهُ وَرَسُولُهُ وَالَّذِينَ آمَنُوا الَّذِينَ يُقِيمُونَ الصَّلَاةَ وَيُؤْتُونَ الزَّكَاةَ وَهُمْ رَاكِعُونَ
وَمَن يَتَوَلَّ اللَّهَ وَرَسُولَهُ وَالَّذِينَ آمَنُوا فَإِنَّ حِزْبَ اللَّهِ هُمُ الْغَالِبُونَ
يَا أَيُّهَا الَّذِينَ آمَنُوا لَا تَتَّخِذُوا الَّذِينَ اتَّخَذُوا دِينَكُمْ هُزُوًا وَلَعِبًا مِّنَ الَّذِينَ أُوتُوا الْكِتَابَ مِن قَبْلِكُمْ وَالْكُفَّارَ أَوْلِيَاءَ ۚ وَاتَّقُوا اللَّهَ إِن كُنتُم مُّؤْمِنِينَ
وَإِذَا نَادَيْتُمْ إِلَى الصَّلَاةِ اتَّخَذُوهَا هُزُوًا وَلَعِبًا ۚ ذَٰلِكَ بِأَنَّهُمْ قَوْمٌ لَّا يَعْقِلُونَ
O those who believe, do not take the Jews and Christians for intimate friends. They are friends to each other And whoever takes intimate friends from them, he is one of them. Surely, Allah does not take the unjust people to the right path. 
Now, you see those who have disease in their hearts race towards them saying, "We apprehend that some misfortune may overtake us." So, it is likely that Allah may bring victory or a command from His own side, whereupon they become regretful over what they concealed in their hearts. 
And those who believe will say, "Are these the ones who swore by Allah on emphatic oaths that they were with you?" Their deeds have gone waste; hence they became losers. 
O those who believe, whoever of you turns back from his Faith, then, Allah shall bring a people whom He loves and who love Him, soft on the believers, hard on the disbelievers, who fight in the way of Allah and are not afraid of the reproach of any critic. That is a grace of Allah. He confers it on whom He wills. And Allah is All-Embracing,All-Knowing. 
Your only friend is Allah, and His Messenger,and those who believe those who establish Salah and pay Zahah and bow before Allah.  And whoever takes to friendship with Allah and His Messenger and those who believe, then, the people of Allah are the ones to prevail. 
O those who believe, do not take as friends those who have taken your Faith in jest and fun, those who have been given the Book prior to you, and the disbelievers. And fear Allah, if you are believers. 
And when you call for salah , they take it in jest and fun. That is because they are a people who do not understand. 
Explanation in Brief
The verses cited above take up three important subjects which are the basic principles of unity among Muslims as a collectively organized community.
1. Muslims can deal with non-Muslims in the spirit of tolerance, sympathy, goodwill, equity,justice, favour and kindness, almost everything within that line of conduct. In fact, they should do that for they have been taught to do that. But, what is not permitted is the kind of fast friendship and indiscriminating intimacy which may garble the distinctive hallmarks of Islam. This is the issue known as the 'Tark al-Muwalat' to refrain from deep (friendship)in Islamic terminology.
The second principle stressed upon is that should the Muslims of any time and place shift away from the first principle stated above and develop an intimacy of this nature with non-Muslims, then, let them not be under the impression that their conduct could harm Islam in any manner whatsoever because Allah Almighty has Himself taken the responsibility of seeing that Islam remains duly protected. It cannot be eliminated by anyone. However, if a set of people still go out of their minds, break the limits of Islamic modality of doing things and, let us presume, decide to leave the very pale of Islam, then, Allah Ta'ala will bring in another set of people who will uphold and establish the principles and laws of Islam.
3. Once we know the positive and negative aspects in perspective, it becomes evident that the real friendship of a Muslim deep, intense, profound and reliance-worthy can only be with Allah, the Highest of the high, His Messenger, and with those who believe in them.
After this brief introduction of the subject, we can now move to the detailed explanation of the verses.