Cheese is complex halachically. While some authorities permit drinking chalov stam (and using it to make cheese), NO authorities (to my knowledge) allow gevinas akum. A Jew MUST be present during the cheese-making process.
Even non-cholav-Yisroel cheeses must be made under the supervision of a Jew in order to be certified Kosher. There are a number of brands that make cheese with non-cholav-Yisroel milk, as it is substantially cheaper. But they all are Gevinas Yisroel.
I'm not a rabbi but this is my understanding of the situation.