As Shalom explained in his answer to a question about chalav Yisrael milk, R' Moshe Feinstein ruled that in countries where the local government regulations are sufficient to ensure that cow's milk is not tainted with the milk of non-kosher animals, any milk can be considered chalav Yisrael even if there was no Jew supervising the milking of the animals.
Not everybody accepts this leniency and those who do not are careful to only consume dairy products whose production was directly supervised by a Jew. Logically, those who do not accept the leniency would consider the dairy to be completely non-kosher (as Shalom said, "Today we speak of 'chalav ha-companies', or 'chalav stam', which means: 'milk whose status is viewed as chalav yisrael by some, and chalav akum by others'").
Yet I know that there are people who do not accept R' Moshe's leniency about chalav stam being kosher, though they are not careful to avoid dairy products served, prepared, or cooked on equipment that has been used for chalav stam. What is the justification for eating chalav stam-equipment foods if chalav stam is considered not kosher?
(I asked this question to someone I know who does this and he said he doesn't know how it's justified. He does it because he otherwise wouldn't be able to eat at his in-laws' house so his rav gave him permission).