Is difference of opinion allowed in Islam?

In a nutshell - yes. There are 2 distinct methodologies or approaches to understanding texts: Literal Metaphorical Both approaches are valid and it is why we have 4 fiqh schools. Bot approaches existed amongst the sahaba during the time of the Prophet (saw) and he allowed it. عَنِ ابْنِ عُمَرَ ـ رضى الله عنهما ـ قَالَ قَالَ النَّبِيُّ صلى الله عليه وسلم يَوْمَ الأَحْزَابِ ‏ "‏ لاَ يُصَلِّيَنَّ أَحَدٌ الْعَصْرَ إِلاَّ فِي بَنِي قُرَيْظَةَ ‏"‏‏.‏ فَأَدْرَكَ بَعْضُهُمُ الْعَصْرَ فِي الطَّرِيقِ، فَقَالَ بَعْضُهُمْ لاَ نُصَلِّي حَتَّى نَأْتِيَهَا‏.‏ وَقَالَ بَعْضُهُمْ بَلْ نُصَلِّي، لَمْ يُرِدْ مِنَّا ذَلِكَ، فَذُكِرَ ذَلِكَ لِلنَّبِيِّ صلى الله عليه وسلم فَلَمْ يُعَنِّفْ وَاحِدًا مِنْهُمْ‏.‏ On the day of Al-Ahzab (i.e. Clans) the Prophet (saw) said, "None of you should offer the Asr prayer but at Banu Quraiza's place." The Asr prayer became due (and the time for Asr was finishing). Some companions (took the command literally) and said, "We will not offer it till we reach it, the place of Banu Quraiza." While others (looked at the meaning of his command) said, "No, we will pray at this spot, for the Prophet (saw) did not mean that for us." (i.e., the Prophet meant hurry up). Later it was mentioned to the Prophet (saw) and he did not rebuke either of the two groups." (Sahih al-Bukhari) عَنْ عَائِشَةَ، رضى الله عنها أَنَّ بَعْضَ، أَزْوَاجِ النَّبِيِّ صلى الله عليه وسلم قُلْنَ لِلنَّبِيِّ صلى الله عليه وسلم أَيُّنَا أَسْرَعُ بِكَ لُحُوقًا قَالَ ‏ "‏ أَطْوَلُكُنَّ يَدًا ‏"‏‏.‏ فَأَخَذُوا قَصَبَةً يَذْرَعُونَهَا، فَكَانَتْ سَوْدَةُ أَطْوَلَهُنَّ يَدًا، فَعَلِمْنَا بَعْدُ أَنَّمَا كَانَتْ طُولَ يَدِهَا الصَّدَقَةُ، وَكَانَتْ أَسْرَعَنَا لُحُوقًا بِهِ وَكَانَتْ تُحِبُّ الصَّدَقَةَ‏ "Some of the wives of the Prophet (saw) asked him, "Who amongst us will be the first to follow you (i.e., die after you)?" He said, "Whoever has the longest hand." So they started measuring their hands with a stick and Sauda's hand turned out to be the longest. (However Zainab bint Jahsh died first of all in the caliphate of Umar), so we came to know that the long hand was a symbol of practicing charity, so she was the first to follow the Prophet (saw) and she used to love to practice charity." (Sahih al-Bukhari)