Starting and ending
I'm going to start learning German on Duolingo but I want to stop learning French. Is it possible to stop a language at duo?
I do not see how you lose your data.
You will "clear your tree" if you wish to, which means you get to start going through your tree again.
Having a "golden" tree is not where your knowledge sits.
It is what is in your brain where you want your language knowledge to sit.
Attaining and then more importantly maintaining a golden tree is one vehicle you can use to help get the knowledge into your brain, so that it moves from your conscious part of thinking, to your unconscious part. So that you can talk in a language.
People who are able to talk in a language have studied it enough to get it over the threshold of consciously understanding a language, such that it has become part of their unconscious mind. So that they are able to hold a conversation - to listen as well as to speak - with their conscious mind, while it is their unconscious mind that works out how to do all this.
There is some fascinating information out there about how all this works.
So - it is quite fine to clear / delete a language in Duolingo.