What is the ruling on dealing with students who are people of innovation (Ahl al-Bid'ah) in academic matters, and is it permissible to benefit them financially, or to backbite and speak ill of them?

The treatment of innovators (Ahl al-Bid'ah) in matters unrelated to their innovation is evaluated based on benefit (maslahah) and harm (mafsadah). If shunning them deters their innovation, then they should be shunned. However, if interacting with them opens a door for their guidance, then they should be interacted with. This includes financial transactions.

It is stated in the Fiqh Encyclopedia that a non-public innovator should be advised, not shunned, whereas it is sunnah to shun a public innovator.

Backbiting innovators is not permissible, with the exception of speaking about their specific innovation, if they are known for it, for the purpose of warning and advising.