Bacteria can't live in a soaps ph range of 9.5 to 10.5
The thing that makes creams go off are contamination of the soap. This is why it's advised you bowl lather creams. If you lather direct from a tub of cream soap the water will reduce the ph level slightly and can make the environment bacteria friendly. This is ok if you use the soap daily but if you then put it away in a cupboard the nasties have a chance to multiply. Oh and bacteria does not have a smell at unsafe levels, I can't remember the count but it's extremely high before it will give off a smell.
This is why some cream soaps have preservatives in them.
A rancid smelling cream soap is something entirely different, this is the free oils oxidizing which means they are breaking down, decomposing.
All these things you don't normally see with hard soaps. This is because the salts of hard soap are more densely packed which protects the soaps ph level and free oils.