Given the right circumstances, any milk or cream product will curdle (a process in which the curd protein, casein, coagulates and forms clumps). Acid, heat, and salt are the antagonists, all of which cause curdling. The milk has only one defense mechanism, which you don’t want to hear about – fat. The more fat it contains (and the fresher it is), the less likely it is to curdle. There is a dramatic difference in the ability of heavy cream vs. light cream to resist curdling. To bring skim milk into the equation is almost asking it to curdle.
But all may not be lost. Your best bet is to prepare the soup without the milk (assuming the base is a stock and not the milk itself), and add the milk at the end of the cooking process. Then make sure not to heat it at all or for long, and don’t let it get above 180°F. Also, add any salt just before serving.