✅Answer: Please pay attention to the following narrations:

1 عَنِ ابْنِ أَبِي عُمَيْرٍ عَنِ ابْنِ بُكَيْرٍ قَالَ سَأَلَ زُرَارَةُ أَبَا عَبْدِ اللَّهِ عَنِ الصَّلَاةِ فِي الثَّعَالِبِ وَ الْفَنَكِ وَ السِّنْجَابِ وَ غَيْرِهِ مِنَ الْوَبَرِ فَأَخْرَجَ كِتَاباً زَعَمَ أَنَّهُ إِمْلَاءُ رَسُولِ اللَّهِ أَنَّ الصَّلَاةَ فِي وَبَرِ كُلِّ شَيْ ءٍ حَرَامٍ أَكْلُهُ فَالصَّلَاةُ فِي وَبَرِهِ وَ شَعْرِهِ وَ جِلْدِهِ وَ بَوْلِهِ وَ رَوْثِهِ وَ كُلِّ شَيْ ءٍ مِنْهُ فَاسِدٌ لَا تُقْبَلُ تِلْكَ الصَّلَاةُ حَتَّى يُصَلِّيَ فِي غَيْرِهِ مِمَّا أَحَلَّ اللَّهُ أَكْلَهُ ثُمَّ قَالَ يَا زُرَارَةُ هَذَا عَنْ رَسُولِ اللَّهِ فَاحْفَظْ ذَلِكَ يَا زُرَارَةُ فَإِنْ كَانَ مِمَّا يُؤْكَلُ لَحْمُهُ فَالصَّلَاةُ فِي وَبَرِهِ وَ بَوْلِهِ وَ شَعْرِهِ وَ رَوْثِهِ وَ أَلْبَانِهِ وَ كُلِّ شَيْ ءٍ مِنْهُ جَائِزٌ إِذَا عَلِمْتَ أَنَّهُ ذَكِيٌّ قَدْ ذَكَّاهُ الذَّبْحُ وَ إِنْ كَانَ غَيْرَ ذَلِكَ مِمَّا قَدْ نُهِيتَ عَنْ أَكْلِهِ وَ حُرِّمَ عَلَيْكَ أَكْلُهُ فَالصَّلَاةُ فِي كُلِّ شَيْ ءٍ مِنْهُ فَاسِدٌ ذَكَّاهُ الذَّبْحُ أَوْ لَمْ يُذَكِّهِ.

📚 Al-Kafi, vol. 3, p. 397

Zurarah asked Imam Sadiq (peace be upon him) about praying in the fur of foxes, fennec foxes (which are carnivorous mammals, smaller than foxes, with long ears and reddish fur), squirrels, and other furs. Imam Sadiq (peace be upon him) took out a book that was dictated by the Messenger of God (prayers of God be upon him and his family), and in it was the following:

'Indeed, anything (any animal) whose meat is forbidden to eat, then praying in its fur, hair, skin, urine, droppings, and anything from it is invalid, and that prayer is not accepted until one prays in something else, from what God has made permissible to eat.' Then he said: 'O Zurarah, this is from the Messenger of God (prayers of God be upon him and his family), so preserve it!'

'O Zurarah, if it is from things whose meat is eaten, then praying in its fur, urine, hair, droppings, milk, and anything from it is permissible, provided that it has been purified by (a lawful) slaughter. But if it is from other living beings that you have been forbidden from eating and have been made unlawful for you, then praying in anything from it is invalid, whether it has been purified by slaughter or not!'

2 عَنْ مُحَمَّدِ بْنِ أَحْمَدَ بْنِ يَحْيَى عَنْ عُمَرَ بْنِ عَلِيِّ بْنِ عُمَرَ بْنِ يَزِيدَ عَنْ إِبْرَاهِيمَ بْنِ مُحَمَّدٍ الْهَمَذَانِيِّ قَالَ: كَتَبْتُ إِلَيْهِ يَسْقُطُ عَلَى ثَوْبِيَ الْوَبَرُ وَ الشَّعْرُ مِمَّا لَا يُؤْكَلُ لَحْمُهُ مِنْ غَيْرِ تَقِيَّةٍ وَ لَا ضَرُورَةٍ فَكَتَبَ لَا تَجُوزُ الصَّلَاةُ فِيهِ.

📚 Al-Tahdhib, vol. 2, p. 209-819

Ibrahim ibn Muhammad said: 'I wrote to the Imam (peace be upon him): 'Hair and fur from things whose meat is not eaten fall on my clothes, and there is no Taqiyyah (precautionary dissimulation) or necessity. (What is the ruling?)' He said: 'Praying in it is not permissible.'

3 عَنْ عَلِيِّ بْنِ أَحْمَدَ عَنْ مُحَمَّدِ بْنِ أَبِي عَبْدِ اللَّهِ عَنْ مُحَمَّدِ بْنِ إِسْمَاعِيلَ بِإِسْنَادِهِ يَرْفَعُهُ إِلَى أَبِي عَبْدِ اللَّه قَالَ: لَا تَجُوزُ الصَّلَاةُ فِي شَعْرِ وَ وَبَرِ مَا لَا يُؤْكَلُ لَحْمُهُ لِأَنَّ أَكْثَرَهَا مُسُوخٌ.

📚 Ilal al-Shara'i, p. 342, hadith 1, chapter 43

Imam Sadiq (peace be upon him) said: 'Praying in the hair and fur of things whose meat is not eaten is not permissible because most of them are from those who were transformed!'

✅ It is clear from the above narrations and their likes that the presence of dog and cat hair on a worshiper's clothes invalidates the prayer and is not permissible, because they are from animals whose meat is forbidden to eat.

Praying in clothes with cat hair stuck to them

اللَّهُمَّ فَصَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ