React not rerendering after mobx observer change

Your code looks sound. I think you have stumbled upon an issue discussed in the How to (not) use decorators part of the documentation. It is important that transform-decorators-legacy is first in the list of babel plugins.

My problem was the order of wrapping the component, because I was using Material UI framework.

Wrong:

export inject('store')(observer(withStyles(styles)(MyComponent)));

Correct:

export withStyles(styles)(inject('store')(observer(MyComponent)));

So, it's important the order with MobX and React Material UI.

if you use the latest version of mobx, and babel version 7.12 add this to you constructor

makeObservable(this)