What is the ruling on designing and overseeing the construction of a mosque for some people of innovation?

The condition set by the endower is only to be acted upon if it is legally permissible. It is not permissible to build a mosque for innovators (Ahl al-Bid'ah) who are considered disbelievers due to their innovation, such as those who curse the Companions considering it lawful, or those who claim the distortion of the Qur'an. Nor is it permissible to oversee their mosque. If the condition set by the endower is not permissible, then it is not allowed to act upon it. The responsible authority may change the condition of the endower to what is more beneficial if the interest (maslaha) dictates it.