I solved this problem. The reason of this error? I dont have an accurate answer, but this is what I have done:
I created a new React-Native project from scratch using Expo.
Installed Firebase (npm i firebase)
Run the project and it worked without any error.
My main project is almost new as well though, so I tried to see the differences between both but they don’t have in fact many differences.
Well, long story short…
Finally I took all the files from my original project (except for node_modules) and put in a different folder with another name. Then it works. Moving file to another folder or changing the name of the original folder works.
My theory is that there is some kind of conflict with Git (Bitbucket in my case)… because even if I try to create a React-Native project from scratch inside my original project folder (an empty folder), it throws the same asyncStorage = null error when installing firebase.
So… I created a new Bitbucket project, and moved my old files to this new repository. Otherwise you change the name of the root folder to any name. Changing the repository worked for me, and keeping the same root folder name worked for me.