Yes. Your policy has certain implications about who you will and will not do business with, but you are entitled to make those choices.
To refine it a bit more closely, some banks require a U.S. taxpayer identification number. The CIP regulation only requires an identifying number and provides examples of foreign numbers that are acceptable. A decision to require a U.S. TIN has even more specfic implications than requiring U.S. ID; i.e. I can have U.S. ID, but still not have a U.S. TIN.
Requiring both U.S. ID and a U.S. TIN sends a pretty specific message.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.