I’ve never heard anyone argue against personal property. Usually the difference is that Anarchists want to skip the workers’ state, while other Communists think it’s a necessity to achieve Communism.
I have the feeling most people cling to free will as a concept because not having free will raises questions if a “self” truly exists. However the existence of free will can be as scary if not more, since how could we define a “self” if it could freely do something not based on what defines it.