Why certain cheeses are a problem and others are not

Gevinat Akum includes some cheeses, but not others. How does that work?

I’ve been asked this many times. Hopefully the following will explain it

There’s a vast scale of what might be considered gevina. It spans from hard cheeses that are aged for years, to standard cheeses,  to yogurts and sour cream. Anything that is from milk that you add a bit of an acidic component to it, and then it curdles a bit, might be called gevina.

Some Rabbanim forbade yogurt as if it were gevina.
My father’s position is that yogurts and sour creams are clearly not gevina. So where do you draw the line.
His view is that gevina is something that requires the use of rennet. Yes, you can use rennet in the process of making cream cheese, but most companies do not. It isn’t necessary. You can control the cheesing process with any basic enzyme or acidic ingredient.
The way to determine what is gevina, according to my father, is to look to the major manufacturers of that item. If mostly they do not use animal rennet, you can assume that it doesn’t really require it and is therefore not gevina as described in the Gemara. Gevina of the Gemara is referring specifically to cheeses that are exclusively animal rennet products. Yes, sometimes someone might make it with Assabim (vegetarian), but that would be an extreme exception to the rule.
When they had gevina made with an alternative rennet from Assabim, it was unique. Almost everyone used real rennet. It’s very difficult to make the cheese the right way (in the olden days) with alternative vegetarian rennet.
Today, there’s a big vegetarian market, so you will find almost every cheese with a vegetarian alternative. But the main bulk of the market will be done the right way with animal rennet.
Cheeses that the bulk of the market uses vegetarian rennet are not gevina, they’re more like yogurts.
I appreciate good cheeses. The typical cheeses they sell here in the US are not cheese. American cheese, Colby jack, mozzarella etc  Gevina refers to a specific type of cheese that is usually very hard and aged and takes an intensive process to create. Those cheeses were almost always made with animal rennet. No self respecting cheese maker would use anything else, and therefore the Chachamim made a gezera for that gevina.
Today, the word “cheese” has expanded to include much more than the original gevina, and would not be included in the gezera.
The ones that disagree with this would have to worry about sour cream and yogurt, because where do you draw the line?!
I hope this clarifies it for you.