[Depositing in Usurious Banks1]

The answer—and Allah is the granter of success: What appears is that there is no objection to depositing in usurious banks if the matter is as mentioned in the question, and depositing is not considered prohibited assistance.
The proof: The Prophet—May Allah bless him and his family and grant them peace—used to transact with the Jews in buying and selling, despite knowing that they consumed ribā and dealt in it and consumed illicit gain; likewise the Companions. That was not considered assistance in ribā.
One may also adduce His saying, Most High: “And among the People of the Scripture is he who, if you entrust him with a great sum, he will return it to you; and among them is he who, if you entrust him with a [single] dinar, he will not return it to you unless you are constantly standing over him.” [Āl ʿImrān:75]. From this verse is taken the permissibility of depositing with the People of the Scripture, even while knowing that they deal in ribā.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2