Adjectives imply something unusual, something different from the standard object the noun refers to. If we say "cheese" for the animal product and "vegan cheese" for the plant product, we implicitly send the message the animal product is normal and the plant product is abnormal.
Strike that. Reverse it.
Say "milk" for plant-based emulsions and "cow milk" for stolen baby cow food. SAy "burger" for veggie protein patties and "cow/pig/turkey burger" for dead rotting animal flesh.
The meat industry doesn't get to control your language.
Words are activism.
Based take. I already use these in daily conversation and don't even think about adding vegan before it. It does help that most people know that I'm vegan though. I'll make sure to add "cow", "chicken", whatever, where applicable moving forward