GameObjectがActiveならFindObjectsOfType()で済みますが、非活性だと取得できません。
そこで非活性なものまで含めて取得できるコードを書きました。

#コード

MyGameObjectUtility.cs

using System.Collections.Generic;
using System.Linq;
using UnityEngine.SceneManagement;

public static class MyGameObjectUtility
{
    // 通常trueしか指定しないのでデフォルト引数をtrueにしてます
    public static T[] GetComponentsInActiveScene<T>(bool includeInactive = true)
    {
        // ActiveなSceneのRootにあるGameObject[]を取得する
        var rootGameObjects = SceneManager.GetActiveScene().GetRootGameObjects();

        // 空の IEnumerable<T>
        IEnumerable<T> resultComponents = (T[])Enumerable.Empty<T>();
        foreach (var item in rootGameObjects)
        {
            // includeInactive = true を指定するとGameObjectが非活性なものからも取得する
            var components = item.GetComponentsInChildren<T>(includeInactive);
            resultComponents = resultComponents.Concat(components);
        }
        return resultComponents.ToArray();
    }

    // 1つだけ取得したい場合はこちら（GetComponentsInActiveSceneを元にして書いたので少し非効率です）
    public static T GetComponentInActiveScene<T>(bool includeInactive = true)
    {
        // ActiveなSceneのRootにあるGameObject[]を取得する
        var rootGameObjects = SceneManager.GetActiveScene().GetRootGameObjects();

        // 空の IEnumerable<T>
        IEnumerable<T> resultComponents = (T[])Enumerable.Empty<T>();
        foreach (var item in rootGameObjects)
        {
            // includeInactive = true を指定するとGameObjectが非活性なものからも取得する
            var components = item.GetComponentsInChildren<T>(includeInactive);
            resultComponents = resultComponents.Concat(components);
        }
        return resultComponents.First();
    }
}

#使用例
ゲーム中というよりは、主にInspectorの参照を取得する際に使用するのを想定してます。

MenuButtonsHandler.cs

using UnityEngine;

public class MenuButtonsHandler : MonoBehaviour
{
    [SerializeField] MenuContentHandler[] MenuContentHandlers;

    // Scriptをアタッチした際に自動で呼ばれる, Inspectorからも呼べる
    private void Reset()
    {
        MenuContentHandlers = MyGameObjectUtility.GetComponentsInActiveScene<MenuContentHandler>();
    }
}

UiHub.cs

using UnityEngine;

public class UiHub : MonoBehaviour
{
    public static UiHub Instance;

    public PartyScrollHandler PartyScrollHandler;
    public PartyEditView PartyEditView;
    public HolderScrollHandler HolderScrollHandler;
    public EquipmentEditScrollHandler EquipmentEditScrollHandler;
    public SummonScrollHandler SummonScrollHandler;
    public UnitCardScrollHandler UnitCardScrollHandler;
    public ComposeView ComposeView;
    public ResultInfoWindow ResultInfoWindow;
    public ComposeOptionSelectScroll ComposeOptionSelectScroll;
    public ComposeOptionConfirmScroll ComposeOptionConfirmScroll;
    public AdventureScrollHandler AdventureScrollHandler;
    public BattleLogScrollHandler BattleLogScrollHandler;
    public JobScrollHandler JobScrollHandler;
    public MessageWindow MessageWindow;
    public DungeonScrollHandler DungeonScrollHandler;

    private void Awake()
    {
        Instance = this;
    }

    private void Reset()
    {
        PartyScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<PartyScrollHandler>();
        PartyEditView = MyGameObjectUtility.GetComponentInActiveScene<PartyEditView>();
        HolderScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<HolderScrollHandler>();
        EquipmentEditScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<EquipmentEditScrollHandler>();
        SummonScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<SummonScrollHandler>();
        UnitCardScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<UnitCardScrollHandler>();
        ComposeView = MyGameObjectUtility.GetComponentInActiveScene<ComposeView>();
        ResultInfoWindow = MyGameObjectUtility.GetComponentInActiveScene<ResultInfoWindow>();
        ComposeOptionSelectScroll = MyGameObjectUtility.GetComponentInActiveScene<ComposeOptionSelectScroll>();
        ComposeOptionConfirmScroll = MyGameObjectUtility.GetComponentInActiveScene<ComposeOptionConfirmScroll>();
        AdventureScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<AdventureScrollHandler>();
        BattleLogScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<BattleLogScrollHandler>();
        JobScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<JobScrollHandler>();
        MessageWindow = MyGameObjectUtility.GetComponentInActiveScene<MessageWindow>();
        DungeonScrollHandler = MyGameObjectUtility.GetComponentInActiveScene<DungeonScrollHandler>();
    }
}