Yes, but freeze in ice cubes trays, and then transfer to suitable containers. Otherwise you will have a large frozen block of soup that will take ages to defrost
Sweet potato and butternut squash soup is one of our favourites and I've frozen loads of it over the years and have never had any problem. What is supposed to happen to it?
Squash doesn't freeze well but squash soup freezes fine. Just divide the soup up into portions that work for you; about 300ml per person is about right for a portion.
Ice cube trays seems a bit extreme and a complete faff IMHO!