Don't throw the baby out with the bathwater. Don't upset the apple cart. These two sentences are:

Question

Quizplus · Accepted Answer

Don't throw the baby out with the bathwater means that you should not get rid of valuable things or ideas in an attempt to get rid of what is not wanted.
Don't upset the apple cart means that you shouldn't cause trouble, especially if it involves spoiling someone's plans.
These meanings are not related to each other so they are neither similar nor contradictory.

Don't Throw the Baby Out with the Bathwater