Is it permissible to perform circumambulation (Tawaf) on a camel nowadays, taking into consideration the pollution of the place and the difficulty of the animal entering the mosque, and was the Prophet's —peace and blessings be upon him— doing so due to an excuse that people should follow?

It is permissible to perform Tawaf while riding a camel, as the Prophet, peace and blessings be upon him, performed Tawaf on a camel during the Farewell Pilgrimage. The jurists have agreed on the permissibility of a rider performing Tawaf for one who has an excuse, but they differed concerning one who does not have an excuse. It is disliked to bring animals into the mosque for fear of defiling it, and while this is not forbidden, the situation of the Sacred Mosque has changed now, so bringing a camel into it is impossible and would lead to harms.