A script to fix the horizontal FOV/orthographic size of a camera to a specified value in Unity

HorizontalCamera.cs

using UnityEngine;

[ExecuteInEditMode]
[RequireComponent( typeof( Camera ) )]
public class HorizontalCamera : MonoBehaviour
{
	private Camera m_camera;
	private float lastAspect;

#pragma warning disable 0649
	[SerializeField]
	private float m_fieldOfView = 60f;
	public float FieldOfView
	{
		get { return m_fieldOfView; }
		set
		{
			if( m_fieldOfView != value )
			{
				m_fieldOfView = value;
				RefreshCamera();
			}
		}
	}

	[SerializeField]
	private float m_orthographicSize = 5f;
	public float OrthographicSize
	{
		get { return m_orthographicSize; }
		set
		{
			if( m_orthographicSize != value )
			{
				m_orthographicSize = value;
				RefreshCamera();
			}
		}
	}
#pragma warning restore 0649

	private void OnEnable()
	{
		RefreshCamera();

#if UNITY_EDITOR
		UnityEditor.EditorApplication.update -= Update;
		UnityEditor.EditorApplication.update += Update;
#endif
	}

	private void Update()
	{
		float aspect = m_camera.aspect;
		if( aspect != lastAspect )
			AdjustCamera( aspect );
	}

	public void RefreshCamera()
	{
		if( !m_camera )
			m_camera = GetComponent<Camera>();

		AdjustCamera( m_camera.aspect );
	}

	private void AdjustCamera( float aspect )
	{
		lastAspect = aspect;

		// Credit: https://forum.unity.com/threads/how-to-calculate-horizontal-field-of-view.16114/#post-2961964
		float _1OverAspect = 1f / aspect;
		m_camera.fieldOfView = 2f * Mathf.Atan( Mathf.Tan( m_fieldOfView * Mathf.Deg2Rad * 0.5f ) * _1OverAspect ) * Mathf.Rad2Deg;
		m_camera.orthographicSize = m_orthographicSize * _1OverAspect;
	}

#if UNITY_EDITOR
	private void OnValidate()
	{
		RefreshCamera();
	}

	private void OnDisable()
	{
		UnityEditor.EditorApplication.update -= Update;
	}
#endif
}

How To

Simply add this component to your camera and tweak its FOV/orthographic size.