Here's the detailed explanation:
As you take the curd mass and put it in contact with the edge of the cheesecloth, there are both dissolved ions and charged micelle particles that mechnanically become embedded in the threads of the cloth. The smaller the thread count, the larger the openings between threads, which is great for water drainage. It's also great for particles to attach themselves and stick all around the individual threads. And once they attach in the beginning of a cheesemake, they stay there. So back to the curd mass. Now you have a charged layer sticking to the cloth, and charged particles in the curd mass. Well, they will stick together when they come in contact, and stick more with time, heat, and pressure. End result is you have a fused curd to the cheesecloth.
The two mitigation steps here, maybe three are to use a high quality cloth with a high threadcount, but not so high as the water can't drain. Butter muslin is about right, or maybe something a little less intensive. This will make a difference because it presents oriented threads, and cotton of a high quality that works better. The second mitigation approach is to ionically "neutralize", that is, bring into a state of equilibrium so that the cheesecloth cannot fuse well to the curd. This is done by ensuring a low calcium content, and high acid content. The acid will help to degrade the micelles on the outer curd to the point where fusing is less likely. That is, soak in whey, which already has high acid and low calcium.
Alpine styles fuse more because the outer k-casein shell on the micelle has more phosphate available that has not yet been bound up by acid. It literally is ionically glued together.
So Sailor is right, although a high threadcount cloth does help, the acidity and calcium make a bigger difference.
Oh and the third approach is to use synthetic cloth, such as plyban.