Jason here from Shopify Support.
From Moneris's document, it states that Moneris processes and settles all UnionPay transactions in Canadian dollars, meaning it accepts UnionPay credit/debit cards. Here's more information on UnionPay/Moneris gateway. I cross checked on UnionPay's website, Moneris is listed as one of its partners.
Feel free to contact the Moneris support to clarify if UnionPay is accepted with your account.
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All the best,