Is it considered an innovation (bid‘ah) to deviate from the well-known post-prayer remembrances, and is it permissible to go to the Budshishiyya zawiya to perform prayers there despite the presence of a closer mosque?

What the aforementioned group does involves two matters that contravene the Sunnah of the Prophet: firstly, their adherence to a dhikr (remembrance) after the prayer that is not among the prescribed adhkar (plural of dhikr) for that time; and secondly, their communal recitation of that dhikr and supplication after the obligatory prayer. This falls under the category of bid‘ah idafiyah (additive innovation). Therefore, we advise you to limit your prayers to the mosque closest to your home, especially if it has a larger congregation, and not to go to the mentioned zawiyah (religious lodge). You should also advise these individuals of the necessity of abandoning their religious innovations, doing so with wisdom and gentleness.