Question:

Can we open bank accounts, and use credit cards?

Answer:

Generally speaking, the ulema have said one should avoid
these actions, as they aid in haram (riba). Some of the ulema (like bin baz)
have given the ruling that one is given a leeway (rukhsa) under certain
circumstances, if it is a neccessity and one would face difficulty without
doing it. The leeways vary in accordance to the degree of difficulty,
like starvation for eating pork, and “zero” difficulty for shortening the salat while travelling.

In the case of bank accounts and credit cards, some of the ulema have ruled in the case of
difficulties such as the difficulty of transferring wealth, or in safeguarding
wealth in the case that there is a good chance it would be stolen, one would be
given a leeway to deposit the wealth in the account, however not for a prolonged
time.  See the chapter on rulings for banks, in the book Fatawa Islamiyah, volume 3 . 

Some of the ulema have expressed their liking to use a “debit” cards
instead of “credit” cards.

It is incumbant for everyone to listen and learn from the Rukhass (leeways) that the
ulema explain to us, and not be arrogant, antagonist, and extremist. The ulema
are the people of knowledge, and they are teaching the correct explanation of the
sayings of prophet Muhammed, may Allah’s peace and blessings be upon him, and the
commandments of Allah.

And Allah knows best.

–Shaikh Sajid