Why do my Radio buttons state not updating? – Flutter

1. When you want the state of widget to change you should be using stateful widget and not stateless widget.
2. To change the state of the widget in stateful widget you should use function setState.

Your modified working code:

import 'package:flutter/material.dart';
import 'package:get/get.dart';

void main() => runApp(GetMaterialApp(home: Home()));

class Controller extends GetxController {
  var gender = "F".obs;

  void onChangedGender(String? value) {
    gender = (value ?? "M").obs;
    print(gender.value);
  }
}

class MyWidget extends StatefulWidget {
  const MyWidget({super.key});

  @override
  State<MyWidget> createState() => _MyWidgetState();
}

class _MyWidgetState extends State<MyWidget> {
  @override
  Widget build(context) {
    final Controller c = Get.put(Controller());
    return Scaffold(
      body: Center(
        child: SizedBox(
          width: 400,
          child: Obx(
            () => Row(
              children: [
                Expanded(
                  child: RadioListTile(
                    value: "M",
                    groupValue: c.gender.value,
                    title: const Text("Male"),
                    onChanged: (val) {
                      setState(() { c.onChangedGender(val); }); 
                      },
                  ),
                ),
                Expanded(
                  child: RadioListTile(
                    value: "F",
                    groupValue: c.gender.value,
                    title: const Text("Female"),
                    onChanged: (val) {
                      setState(() { c.onChangedGender(val); }); 
                      },
                  ),
                ),
              ],
            ),
          ),
        ),
      ),
    );
  }
}


class Home extends StatelessWidget  {
    @override
  Widget build(context) {
    return MyWidget();
    }
}