rebdoniel -“Hot coffee can be consumed in any establishment, especially in a disposable cup. Sugar and milk in DD shops both generally have hechsherim, and many hold that both these items in America don’t require a hechsher anyways.”
I don’t know about Treif DD’s shops, but I do know about Starbucks. The cRc posts on their website -that one should Not buy hot coffee in a Starbucks that sells Treif sandwiches. We had this discussion a few times in the CR. The same could be for Treif DD’s. And even if R’ Abadi (& of course our own PBA) holds differently -he is a Daas Yochid. So unless you’re Talmidim of him -Do Not drink coffee from anywhere. Or you can ask your LOR what to do.
I personally think people come here in the first place to ask Shailos because they are looking for Kulos, instead of asking their LOR!