How can I detect the clicking of a tab button in Xamarin.Forms?

I know you want to avoid using custom renderers, but this is only possible by using a Custom Renderer.

Code

Xamarin.Android Custom Renderer

using Android.Content;
using Android.Support.Design.Widget;

using Xamarin.Forms;
using Xamarin.Forms.Platform.Android;
using Xamarin.Forms.Platform.Android.AppCompat;

[assembly: ExportRenderer(typeof(MainPage), typeof(MainPageRenderer))]
namespace YourNameSpace
{
    public class MainPageRenderer : TabbedPageRenderer, TabLayout.IOnTabSelectedListener
    {
        MainPage _page;

        public MainPageRenderer(Context context) : base(context) { }

        protected override void OnElementChanged(ElementChangedEventArgs<TabbedPage> e)
        {
            base.OnElementChanged(e);

            if (e.NewElement != null)
                _page = e.NewElement as MainPage;
            else
                _page = e.OldElement as MainPage;
        }

        void TabLayout.IOnTabSelectedListener.OnTabReselected(TabLayout.Tab tab)
        {
            System.Diagnostics.Debug.WriteLine("Tab Reselected");
            //Handle Tab Reselected
        }
    }
}

Xamarin.iOS Custom Renderer

using System;
using System.Diagnostics;

using UIKit;

using Xamarin.Forms;
using Xamarin.Forms.Platform.iOS;

[assembly: ExportRenderer(typeof(MainPage), typeof(MainPageRenderer))]
namespace YourNameSpace
{
    public class MainPageRenderer : TabbedRenderer
    {
        MainPage _page;

        protected override void OnElementChanged(VisualElementChangedEventArgs e)
        {
            base.OnElementChanged(e);

            if (e.NewElement != null)
                _page = e.NewElement as MainPage;
            else
                _page = e.OldElement as MainPage;

            try
            {
                if (ViewController is UITabBarController tabBarController)
                    tabBarController.ViewControllerSelected += OnTabbarControllerItemSelected;
            }
            catch (Exception exception)
            {
                Debug.WriteLine(exception);
            }
        }

        void OnTabbarControllerItemSelected(object sender, UITabBarSelectionEventArgs eventArgs)
        {
            if (_page?.CurrentPage?.Navigation != null && _page.CurrentPage.Navigation.NavigationStack.Count > 0)
            {
                Debug.WriteLine("Tab Tapped");
                //Handle Tab Tapped
            }
        }
    }
}

Code credit: @Kyle https://stackoverflow.com/a/42909203/5953643