Hot soup can go straight into the fridge without cooling it down first.
However it's best to allow the hot soup to cool down for 20 to 30 minutes first and then put it in the refrigerator so that it's not so hot.
When you put hot food into the refrigerator without cooling the food down first it increases the temperature inside the refrigerator which can potentially lead to the spoilage of the other foods.
Your refrigerator will also have to work a bit harder at getting the temperature down.
However there have been times when I got done making hot soup and then had to put some leftover hot soup right into the fridge and it's been okay.
Just like other hot foods that I've had to refrigerate and it's never been a problem.