This is a provider which allows to use mobx-react Provider with wix/react-native-navigation.

MobxRnnProvider.js

import { Provider } from 'mobx-react/native';

const SPECIAL_REACT_KEYS = { children: true, key: true, ref: true };

export default class MobxRnnProvider extends Provider {
  props: {
    store: Object
  };

  context: {
    mobxStores: Object
  };

  getChildContext() {
    const stores = {};

    // inherit stores
    const baseStores = this.context.mobxStores;
    if (baseStores) {
      for (let key in baseStores) {
        stores[key] = baseStores[key];
      }
    }

    // add own stores
    for (let key in this.props.store) {
      if (!SPECIAL_REACT_KEYS[key]) {
        stores[key] = this.props.store[key];
      }
    }

    return {
      mobxStores: stores
    };
  }
}

startApplication.js

import { Navigation } from 'react-native-navigation';
import Provider from './lib/MobxRnnProvider';
import store from './store';
import HomeScreen from './screens/HomeScreen';

export default function startApplication() {
  Navigation.registerComponent('myapp.HomeScreen', () => HomeScreen, store, Provider);
  Navigation.startSingleScreenApp({
    screen: { screen: 'myapp.HomeScreen' }
  });
}

store.js

import AuthStore from './AuthStore';
import UserStore from './UserStore';

export default {
  auth: new AuthStore(),
  users: new UserStore()
};

UserScreen.js

import { Component } from 'react';
import { Text } from 'react-native';
import { inject, observer } from 'mobx-react/native';

@inject('users')
@observer
export default class UserScreen extends Component {
  render() {
    const { users } = this.props;
    return (
       <Text>Users count: {users.length}</Text>
    );
  }
}

I am using registerComponentWithRedux
And it works.

Navigation.registerComponentWithRedux('myapp.HomeScreen', () => HomeScreen, store, Provider);

My package dependencies:
"react": "16.3.1",
"react-native": "0.55.4",
"react-native-navigation": "2.0.2641",
"mobx": "4.3.1",
"mobx-react": "5.1.0"

Thank you @megahertz !