John, you are describing the exact phenomenon I'm talking about!

Now then, here is a link to a website called titled "St. Patrick's Day Fun @ FOUR EYES JOKE SHOP" (though the URL is "newenglandyankee.com).

If you scrowl down, you will find the "Orange Tie Dyed Shirt For non-Irish Celebrants".

I'm guessing it has a little something to do with the custom.

If anyone was looking for demeaning stereotyping of the Irish and Irish Americans, one couldn't find better examples than those exhibited at that website!