Wells Fargo doesn't.
CapitalOne doesn't.
Many times, its dependent on the State/City and the Bank officer whom you encounter when you walk in. To negate it, one has to try many different branches and if possible - in different cities.
And this may hurt some ""touchy"" people here, it also depends on your personality/ the way you are dressed/ the way you talk with the officer dealing with your application.
And finally it also depends on the bank officer dealing with yr application in regards to his /her view on your race/nationality and possible amount of business you may bring in eventually.