Any dairy product will curdle under the right conditions. Acidity, sodium and temperature all play a part in causing the casein, or curd, in milk and cream to coagulate -- good if you're making cheese, not good if you're making cream soup. Classically, cream soups use thickened milk, or bechamel, for the base and heavy cream as the finish ingredient, but cream soups also include purees and stock-based soups that use cream as a finishing ingredient. You have to create conditions unfavorable to casein coagulation at critical points during the cooking process to keep cream soup stabilized.
Mix a few tablespoons of flour with water to make a paste. Whisk the flour paste into the soup a few minutes before you add the acidic ingredients. Starch bonds with the fat in the soup to stabilize it.
Attach a candy thermometer to the pot of soup just before you add the heavy cream. Adjust the temperature on the stove as needed so the temperature of the soup stays between 160 and 170 degrees Fahrenheit. You can also hold a meat thermometer in the center of the soup for about 30 seconds to get a temperature reading.
Pour the heavy cream in a saucepan and set the heat to low. Cream soups usually use a 8:1 ratio of soup to heavy cream, but you can add an extra tablespoon or two if you see you need more later.
Stir the soup and ladle it into the heavy cream a few tablespoons at a time, stirring frequently, to temper it. Temper a cup or two of soup into the heavy cream.
Pour the tempered cream into the soup, a few tablespoons at a time, stirring frequently.
Season the cream soup to taste with kosher salt and white pepper. Taste the soup and examine its mouthfeel. Cream soups should feel velvety, not thick and viscous, on the tongue, and silky smooth, not runny.
Adjust the seasoning, if needed, and add the finishing ingredients. Common finishing ingredients include small dices of the main ingredient, if garnishing a pureed soup, and freshly chopped herbs.