For example, I live in CA but would like to organize my LLC in MT. Do I need to have my business bank accounts set up and linked to a MT address?
Doesnt matter for Federal Income Taxes, Only State Income Taxes. You will have to report the income in the State where you generate the income and reside. So report the income in California. But, If you do conduct business in Montana then you would have to complete a Non-Resident Tax Return.