Is it obligatory to denounce the widespread and fabricated hadiths found in mosques and books, or should that be left to the people of knowledge?

It is not permissible to narrate fabricated hadiths. Whoever knows that a hadith is fabricated must deny its attribution to the Prophet, peace and blessings be upon him. This is not limited to specialists but includes every student of knowledge who becomes aware of it, after reviewing the statements of scholars and consulting them, while observing the etiquette of denouncement and considering the circumstances of the mosque attendees.