The commentary states that dog hide can be purified by tanning because the dog is not treated there as inherently impure like the pig.
وَتُطَهِّرُ الذَّكَاةُ الشَّرْعِيَّةُ جِلْدَ غَيْرِ الْمَأْكُولِ دُونَ لَحْمِهِ عَلَى أَصَحِّ مَا يُفْتَى بِهِ
Proper legal slaughter purifies the hide of a non-edible animal other than the pig, but does not make its meat lawful or pure under the preferred position stated here.
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Purification of Hides and Special Animal Substances
The commentary states that dog hide can be purified by tanning because the dog is not treated there as inherently impure like the pig.
وَتُطَهِّرُ الذَّكَاةُ الشَّرْعِيَّةُ جِلْدَ غَيْرِ الْمَأْكُولِ دُونَ لَحْمِهِ عَلَى أَصَحِّ مَا يُفْتَى بِهِ
Proper legal slaughter purifies the hide of a non-edible animal other than the pig, but does not make its meat lawful or pure under the preferred position stated here.