Anyone who has ever had coffee at starbucks knows that the coffee is always served in paper cups that are thrown away afterwards. Similarly, they do not use spoons btu plastic stirrers. I am at loss to understand the problem. The coffee machines surely are not washed “together’ with anything.
The cRc is apparently asserting that they do wash some of the coffee making equipment together with other utensils. Here’s the link to the OP.
Note that the terminology is vague; they’re not publicly saying that it’s not kosher, just that there is a serious kashrus concern, so ask a competent posek.