Is it permissible to take variable profits from a bank that affirms it operates by Islamic transactions and is completely separate from the usurious branch?

One should not be deceived by the claim that Islamic banks are based on Sharia principles and regulations, and that they have a Sharia supervisory board composed of trusted scholars. It is not possible to definitively declare dealing with these branches as permissible or prohibited without understanding their methodology. If they adhere to the conditions mentioned in the following fatwas (8665, 39504, 41442), then there is no harm in dealing with them. Otherwise, safety is paramount. It is preferable for a Muslim not to deal with interest-based banks at all.