Flutter is not rebuilding same widget with different parameters

your problem in "MyTAbs" passing parameters class

after edit it , now its work

you dont need to pass the date from "Stateful" class to the "State", just call it with "widget.parameterName" in the state your code after edit :

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

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _counter = 0;
  Widget body;
  @override
  void initState() {
//    body = getBody(0);
    super.initState();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
        elevation: 0,
      ),
      body: body,
      bottomNavigationBar: BottomNavigationBar(
          currentIndex: _counter,
          onTap: (index){
            _counter = index;
            setState(() {
              body = getBody(index);
            });
          },items: [
        BottomNavigationBarItem(icon: Icon(Icons.language),title:
        Text('HELLO')),
        BottomNavigationBarItem(icon: Icon(Icons.security),title:
        Text('BYE'))
      ]),
    );
  }
  Widget getBody(int pos){
    if(pos==0){
//      return new Mx(category: 'ALPHA',type: '@',);
      return new MyTAbs(category: 'ALPHA',type: '@',);
    }
    else{

//      return new Mx(category:'BETA',type: '#',);
      return new MyTAbs(category:'BETA',type: '#',);
    }
  }
}
class Mx extends StatelessWidget{
  final String type,category;
  Mx({this.type,this.category});
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      backgroundColor: getColor(),
      body: new Center(
        child: Text(category+' '+type),
      ),
    );
  }
  Color getColor(){
    if(category=='ALPHA'){
      return Colors.red;
    }
    else{
      return Colors.green;
    }
  }
}
class MyTAbs extends StatefulWidget{
  final String type,category;
  MyTAbs({this.type,this.category});
  Tabs createState() => new Tabs();
}
class Tabs extends State<MyTAbs>{


  @override
  Widget build(BuildContext context) {
    print(widget.type);
// TODO: implement build
    return new Scaffold(
      backgroundColor: getColor(),
      appBar: AppBar(
        title: Text(widget.category+' '+widget.type),
      ),
    );
  }
  Color getColor(){
    if(widget.category=='ALPHA'){
      return Colors.red;
    }
    else{
      return Colors.green;
    }
  }
}

Solved this issue by adding new Key as parameter and passed a UniqueKey like

return new MyTAbs(category: 'ALPHA',type: '@',key: UniqueKey(),);

MyTAbs class

class MyTAbs extends StatefulWidget{
  final String type,category;
  final Key key;
  MyTAbs({@required this.key,this.type,this.category});
  Tabs createState() => new Tabs(title: category,type: type,key: key);
}

Tabs class

class Tabs extends State<MyTAbs>{
  final String title,type;
  final Key key;
  Tabs({this.title,this.type,@required this.key});
  @override
  @override
  Widget build(BuildContext context) {
    // TODO: implement build
    return new Scaffold(
      backgroundColor: getColor(),
      appBar: AppBar(
        title: Text(title+' '+type),
      ),
    );
  }
  Color getColor(){
    if(title=='ALPHA'){
      return Colors.red;
    }
    else{
      return Colors.green;
    }
  }
}

little about Key

You can use keys to control which widgets the framework matches up with other widgets when a widget rebuilds. By default, the framework matches widgets in the current and previous build according to their runtimeType and the order in which they appear. With keys, the framework requires that the two widgets have the same key as well as the same runtimeType. more in flutter docs

Change your Tabs class

class Tabs extends State<MyTAbs> {
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      backgroundColor: getColor(),
      appBar: AppBar(
        title: Text(widget.category + ' ' + widget.type),
      ),
    );
  }

  Color getColor() {
    if (widget.category == 'ALPHA') {
      return Colors.red;
    } else {
      return Colors.green;
    }
  }
}

Class State (Tabs) created only once. So after that you can't call constructor with new parameters. But you have access to the widgets' fields