Just to be clear. No one has a "right" to cash a check unless it's drawn on the bank being asked to cash it. Banks accommodate their customers by cashing checks from time to time, but it's not because the law requires it.
Your bank can establish its own policy based on its own risk assessments and business model. Many banks have found it easier to say that they will not cash checks payable to a business regardless of the legal form in which the business is operated. Their reasoning: It can be a challenge to determine whether a given business is operated as a sole proprietorship or by a partnership, LLC, corporation, etc., and they don't want their tellers having to understand whether ABC Plumbing is a sole proprietorship or not.
As Ken Golliher has repeated in these Threads many times: a sole proprietor is in a position to request that his/her customers make checks payable in the business name or to him/her personally. If he/she wants to be able to cash checks received from customers, those checks should be payable to the proprietor, personally.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8