"Kahlúa Original and Kahlúa Flavors are NOT acceptable for a vegan diet. "Kahlúa Ready-To-Drink (RTD's) are also not vegan, since they contain milk and/or milk proteins." ... The sugars used are considered vegan. We do not use white refined sugar.
What makes Kahlua not vegan?
Kahlua uses sugar filtered with bone char
While they don't use any animal derivatives, Kahlua has found that one of their suppliers uses a sugar refining process that is not vegan-friendly.
Is Kahlua vegan?
No, original Kahlúa and Kahlúa products are all explicitly labelled as not vegan. The 'Ready-To-Drink' products are labelled as containing milk or milk proteins, but it's a little less clear why the original drink isn't vegan friendly.