While it is possible to safely freeze cream-based soups, some people may be unhappy with the result when the soup is reheated and is a different consistency than it was prior to freezing. Defrosting leftover milky or creamy soups can result in separation, which changes the soup's texture and appearance.
Cream-based soups can be frozen, but this causes the consistency of the soup to go from smooth and creamy to lumpy and grainy with a somewhat curdled appearance. The taste of the soup is not likely to be affected much by this. Those who are concerned with appearance and texture should set aside some soup prior to adding the cream or milk and freeze those components separately. Then, the milk or cream can be added when needed.