What is the ruling on attending the Friday sermon delivered by an imam who encourages bid'ah (innovations in religion) or mentions weak and fabricated hadiths? And is one who attends it sinful?

If you are afflicted with a mosque that has an innovative (mubtadi') Imam: if his innovation entails disbelief, then it is not permissible to pray behind him. But if his innovation does not entail disbelief, then the preponderant (rajih) opinion is that it is permissible to pray behind him, and the prayer does not need to be repeated. If it is possible to go to another mosque, especially for students of knowledge, that is better, as an act of enjoining good. As for abandoning prayer in the mosque and praying at home, that is impermissible.

Shaykh al-Islam Ibn Taymiyyah stated that praying behind an innovative or wicked Imam is permissible if he is the appointed Imam (Imam al-ratib), and this is the view of the majority of scholars.

It is not permissible to abandon the mosque and leave the sermon if the preacher calls to an innovation or mentions weak hadiths, unless one is knowledgeable and can pray in another mosque, and had previously advised the preacher. It is permissible to interrupt the preacher if he speaks falsehood or calls to polytheism, provided that no discord is caused and the Friday prayer is not missed. The advice to the preacher should be given with gentleness and in a good manner.

If it is possible to go to a mosque free of innovation, then that is good. Otherwise, it is not permissible to abandon congregational prayers (Jumu' and Jama'at), and one must strive in advising and calling (to the truth) with a good approach.