What is the Islamic ruling about the bank or finance company that deals with Riba and Islamic practices?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It is not permissible to establish a company or a bank, which deals in Riba (interest and/or usury). It is also prohibited to participate, support, or be involved in their activities even if they deal with lawful and forbidden transactions, since every Muslim is obliged to seek only lawful earnings and avoid what is forbidden.

Abu Hurayrah reported that the Prophet said: “O people, Allah is Good, and He accepts only that which is good. Allah commanded the believers as He commanded the Messengers, by saying (what means): {O messengers, eat from the good foods and work righteousness. Indeed, I, of what you do, am Knowing.} [Quran 23:51] He also says (what means): {O you who have believed, eat from the good things which We have provided for you...} [Quran 2:172] He, sallallaahu ‘alayhi wa sallam, then mentioned a man who travels a long distance with his hair disheveled and covered in dust, then he raises his hand towards the sky (and supplicates Allah), 'O Lord, O Lord,' while his food is unlawful, his drink is unlawful, and his clothes are unlawful and his nourishment is unlawful. How then would his supplication be accepted?" [Muslim]

Riba is prohibited, so a Muslims is ordered to avoid it in all circumstances and should not cooperate with the one who deals in it.

Allah knows best.