You should move all the code from the componentWillMount to the constructor or componentDidMount.

componentWillMount() is invoked just before mounting occurs. It is called before render(), therefore calling setState() synchronously in this method will not trigger an extra rendering. Generally, we recommend using the constructor() instead. Avoid introducing any side-effects or subscriptions in this method. For those use cases, use componentDidMount() instead. This is the only lifecycle hook called on server rendering.

componentDidMount() is invoked immediately after a component is mounted. Initialization that requires DOM nodes should go here. If you need to load data from a remote endpoint, this is a good place to instantiate the network request. This method is a good place to set up any subscriptions. If you do that, don’t forget to unsubscribe in componentWillUnmount(). Calling setState() in this method will trigger an extra rendering, but it will happen before the browser updates the screen. This guarantees that even though the render() will be called twice in this case, the user won’t see the intermediate state. Use this pattern with caution because it often causes performance issues. It can, however, be necessary for cases like modals and tooltips when you need to measure a DOM node before rendering something that depends on its size or position.

From the official docs

The componentWillMount() life cycle event is actually the correct place to call fetchData() because it is invoked once before the component mounts, this way you can setState do that the data is there when it mounts.

Mounting: componentWillMount

void componentWillMount()

Invoked once, both on the client and server, immediately before the initial rendering occurs. If you call setState within this method,render() will see the updated state and will be executed only once despite the state change.

Whereas componentDidMount() renders after the component had already mounted.

Mounting: componentDidMount

void componentDidMount()

Invoked once, only on the client (not on the server), immediately after the initial rendering occurs. At this point in the lifecycle, you can access any refs to your children (e.g., to access the underlying DOM representation). The componentDidMount() method of child components is invoked before that of parent components.

componentWillMount is one the first function to be run when creating a component. getDefaultProps is run first, then getInitialState then componentWillMount. Both getDefaultProps and getInitialState will be run only if you create the component with the react.createClass method. If the component is a class extending React.Component, those methods won't be run. It is recommended to use componentDidMount if you can instead of componentWillMount because your component can still be updated before componentWillMount and the first render.

You can find more info on the react component lifecycle here

Also, it is recommended to set the state or the default props inside the class constructor or using getDefaultProps and getInitialState.

class MyComponent extends React.Component {
  constructor(props) {
    super(props);
    this.state = { bar: 'foo' };
  }

  static defaultProps = {
    foo: 'bar'
  };
}

EDIT: Here's the component handling login

import React, { Component } from 'react';
import { View, Text, ActivityIndicatorIOS } from 'react-native';
import { bindActionCreators } from 'redux';
import { connect } from 'react-redux';
import * as actionCreators from '../../actions';
import LoginButton from '../../components/Login';
import reducers from '../../reducers';
import { Card, CardSection, Button } from '../../components/common';

class Login extends Component {
  componentDidMount() {
    // If user is already logged in
    if(this.props.auth.loggedIn) {
      // redirect user here
    }
  }

  componentWillReceiveProps(nextProps) {
    // If the user just log in
    if(!this.props.auth.loggedIn && nextProps.auth.loggedIn) {
      // Redirect user here
    }
  }

  render() {
    console.log(this.props.auth);
    const { actions, auth } = this.props;
    var loginComponent = <LoginButton onLoginPressed={() => actions.login()} />;
    if(auth.error) {
      console.log("erreur");
      loginComponent = <View><LoginButton onLoginPressed={() => actions.login()} /><Text>{auth.error}</Text></View>;
    }
    if (auth.loading) {
      console.log("loading");
      loginComponent = <Text> LOL </Text>;
    }
    return(
      <View>
        <Card>
          <CardSection>
            { auth.loggedIn ? this.props.navigation.navigate('Home') : loginComponent }
          </CardSection>
        </Card>
      </View>
    );
  }
}

function mapStateToProps(state) {
  return {
    auth: state.auth
  };
}

function mapDispatchToProps(dispatch) {
  return {
    actions: bindActionCreators(actionCreators, dispatch)
  };
}

export default connect(mapStateToProps, mapDispatchToProps)(Login);