push does not return the array, but the length of it (docs), so what you are doing is replacing the array with its length, losing the only reference to it that you had. Try this:
import {ADD_ITEM} from '../Actions/UserActions'
const initialUserState = {
arr:[]
}
export default function userState(state = initialUserState, action){
console.log(arr);
switch (action.type){
case ADD_ITEM :
return {
...state,
arr:[...state.arr, action.newItem]
}
default:return state
}
}