Thank you very much for sharing your finding. I had to write a small script that ensures the order because every time I run my code the order changes (I think this might be a bug in Unity)

 using System.Collections.Generic;
 using UnityEngine;
 
 public class ForceButtonOrder : MonoBehaviour {
     [Tooltip("list of button names")]
     public List<string> order;
 
     // Use this for initialization
     void Start () {
         for (int i = 0; i < order.Count; i++)
         {
             transform.Find(order[i]).SetSiblingIndex(i);
         }
     }
 }
 

Yes, it's a ridiculous Unity bug.

Even if you are NOT reordering them at RUNTIME, horizontal layout groups sometimes screw the order of elements - so, they get changed from the order seen in the scene in the Editor.

In this simple example I had to just force all elements (there were four) to bne in the right place, doing so at Start() time seems to work. Nice spot by @BUWbrean

 using UnityEngine;
 
 public class BizarreGroupFixer : MonoBehaviour
 {
     // fix absurd Unity bug, which screws the ordering of
     // horizontal groups (perhaps if one is a prefab?)
 
     public Transform a;
     public Transform b;
     public Transform c;
     public Transform d;
     
     void Start()
     {
         a.SetSiblingIndex(0);
         b.SetSiblingIndex(1);
         c.SetSiblingIndex(2);
         d.SetSiblingIndex(3);
     }
 }