If our bank does not cash on-us checks for non-customers, are we in violation of any laws, such as UCC laws? Would there be any laws that would supercede the UCC laws regarding cashing on-us checks for non-customers?

A person presenting a check for payment at your counter is making Demand for Payment. You have a Demand Deposit Account the check is drawn on. You cannot show preference to creditors and by refusing to cash a check just because the presenter doesn't bank with you, may be cause for "wrongful dishonor".

Now the presenter needs to meet all the ID requirements and regular check cashing requirements, and if not you can refuse payment, just not because they don't bank with you.

Your customer is also paying you to handle their banking transactions. It's not the non customer you are providing service to. ITS YOUR CUSTOMER who pays to the bank to handle their banking transactions.

Some banks in major metropolitan areas; e.g. New York, Houston & Chicago that I know of, do not cash on-us checks for non customers. A bank is allowed to require acceptable identification from the payee and some banks in those locales have concluded that there isn't anything that constitutes acceptable identification from a non customer. They appear to have been able to defend that conclusion, but I do not think it would be defensible in mid-America.

The relevant complaints would come from your customers; i.e. the people who wrote the checks and that is a distinct possibility.

You should also consult state law on this.

I thought it was wrongful dishonor only if the demand was made by your customer.

I thought that the check itself was your customer's demand. If I write a check to a merchant, that check is my demand to the bank to pay that merchant the amount listed on the check from the account also listed on said check.