What is the ruling on the prayer of one who led the people in prayer while not in a state of ritual purity, and completed the prayer for fear of confusing the worshippers?

It is not permissible to complete the prayer while in a state of impurity, and you must seek forgiveness and repent. You should have exited the prayer upon remembering the ritual impurity. It is recommended to appoint one of the congregants as a successor. If you did not appoint a successor, they are permitted to appoint one of themselves or pray individually, and their prayer is valid. As for your prayer, it is invalid and must be repeated. A Muslim should respect all their Muslim brothers, especially those who frequent mosques, for "Indeed, the believers are brothers," and "Indeed, the most noble of you in the sight of Allah is the most righteous of you."