It depends on the bank. Some will open accounts for LLCs, some require ID cards for signers and corporate records to show that the person is authorized. It also depends on who is behind the desk, as someone who needs to meet their quotas for the day will be a lot more amenable.

I know this because my sister is a prominent ex-scientologist and they've been harassing her to the point that everything she owns needs to be in a separate LLC.