I'm not sure. It would be the same process as opening a typical bank account, so if you can do one then you can do the other.

Credit unions in the US have affinity requirements. You must be within the affinity group specified in the credit union's charter. You may be allowed to open a credit union account if you also join an organization such as Financial Awareness Network in lieu of the affinity requirement.

Major banks are generally pleased to open accounts for nonresidents, but the "Patriot Act" requires a lot of documentation, possibly more than what you were expecting to have to provide.

Interest on bank or credit union accounts is not taxed in the US if you are a nonresident alien. However, the IRS may suspect you are running a taxable business if it sees frequent deposits (such as you might have if you are using the account to receive payments from US correspondents).