Cursing is disliked against the drunkard and he is not regarded as a non-Muslim
حَدَّثَنَا عَلِيُّ بْنُ عَبْدِ اللَّهِ بْنِ جَعْفَرٍ، حَدَّثَنَا أَنَسُ بْنُ عِيَاضٍ، حَدَّثَنَا ابْنُ الْهَادِ، عَنْ مُحَمَّدِ بْنِ إِبْرَاهِيمَ، عَنْ أَبِي سَلَمَةَ، عَنْ أَبِي هُرَيْرَةَ، قَالَ أُتِيَ النَّبِيُّ صلى الله عليه وسلم بِسَكْرَانَ، فَأَمَرَ بِضَرْبِهِ، فَمِنَّا مَنْ يَضْرِبُهُ بِيَدِهِ، وَمِنَّا مَنْ يَضْرِبُهُ بِنَعْلِهِ، وَمِنَّا مَنْ يَضْرِبُهُ بِثَوْبِهِ، فَلَمَّا انْصَرَفَ قَالَ رَجُلٌ مَالَهُ أَخْزَاهُ اللَّهُ. فَقَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم " لاَ تَكُونُوا عَوْنَ الشَّيْطَانِ عَلَى أَخِيكُمْ ".
Narrated Abu Huraira: A drunk was brought to the Prophet (ﷺ) and he ordered him to be beaten (lashed). Some of us beat him with our hands, and some with their shoes, and some with their garments (twisted in the form of a lash). When that drunk had left, a man said, "What is wrong with him? May Allah disgrace him!" Allah's Messenger (ﷺ) said, "Do not help Satan against your (Muslim) brother."