Is it permissible for someone who follows the Shafi'i school in acts of worship to adopt the Hanafi school's ruling regarding the purification of dog impurity with water only, without earth, especially given that he suffers from obsessive thoughts (waswasah) concerning purity, and would taking this approach invalidate his prayer according to other schools if he prays in clothes purified in this manner?

It is permissible for a person who follows a specific madhhab (definition) (school of thought), such as the Shafi'i, to emulate another madhhab, such as the Hanafi, in a particular issue, without this obligating them to follow the other madhhab entirely. They retain the right to act according to their original madhhab. It has been previously explained that a common person emulates the one they trust most, and that taking the easier opinion for someone afflicted with waswas (obsessive whispering) is not a blameworthy indulgence. The ruling on talfīq (combining different madhhabs) and its controls have also been clarified in previous fatwas.