It’s still a stateless function. It’s impure and produces a side effect but without an internal state )

P.S.

To make it clear you can separate presentation and update. For example, let's move text with a counter to separate widget:

class CounterText extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    var _counter = Provider.of(context).value;
    return new Column(
      mainAxisAlignment: MainAxisAlignment.center,
      children: <Widget>[
        new Text('You have pushed the button this many times:'),
        new Text(
          '$_counter',
          style: Theme.of(context).textTheme.display1,
        ),
      ],
    );
  }
}

In this case, MyHomePage will look like

class MyHomePage extends StatelessWidget {
  MyHomePage({Key key, this.title}) : super(key: key);

  final String title;

  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: new AppBar(
        title: new Text(title),
      ),
      body: new Center(
        child: CounterText(),
      ),
      floatingActionButton: new FloatingActionButton(
        onPressed: () => _incrementCounter(context),
        tooltip: 'Increment',
        child: new Icon(Icons.add),
      ),
    );
  }

  _incrementCounter(context) {
    var appState = Provider.of(context);
    appState.value += 1;
  }
}

and let’s rewrite _incrementCounter as

_incrementCounter(context) {
  Provider.of(context).value += 1;
}

so we have separated presentation and update but we can go future and imagine that +=1 is just a funny way to write message “INCREMENT”

_incrementCounter(context) {
  Provider.of(context).value INCREMENT;
}

Now it looks more familiar to redux dispatch message :)

So I believe now it’s a little bit clear that we have state neither in MyHomePage, not CounterText widgets.