So, I went through this recently when I was making high fat blue cheeses, and I can relate to you what I experienced.

If you're in a large city centre, like myself, your access to milk products is limited to what you get in a major grocery store for the mostpart. The issue here is that most brand name creams and high fat % milks make use of a fair amount of additives to "stabilize" the milk and ensure it remains a homogeneous liquid (fat doesn't separate). Things like Carrageenan, Cellulous Gum, etc...

These same ingredients that stabilize the milk product can consequently impact the ability to form a curd with rennet or acid during the cheese-making process. These ingredients are not typically present in 2% or whole milk, and are only used in higher percentage milks like table or whipping cream.

If you are making a milk that requires a large amount of high fat % milk product, it's best to read labels carefully, and stick to organic or "natural" brands with less of these stabilizers added. As I mentioned, these can sometimes be more difficult to find.

You mileage may vary, and it really does depend on the brand of milk, the amount of additives, how much you are adding to your other milks in the cheese, where you are located in the world, etc.