Not all banks and credit unions provide online access to members, and the law does not require them to do so. Those that provide online access are not required to provide it for free.
The FDIC grants consumers specific rights during banking transactions, and the right to online banking is not one of them. The only consumer right specific to online banking is the Electronic Fund Transfer Act, which protects consumers from fraudulent debit card charges and electronic fund transfers.
All traditional banking laws and rights are applicable to online banking. Banks and credit unions are required to provide adequate security and follow all non-discrimination and credit reporting laws for online transactions.