PerspectiveLock.cs

using UnityEngine;

[ExecuteInEditMode]
public class PerspectiveLock : MonoBehaviour
{
    public Camera _otherCam;
    
    private Camera _cam;
    private Renderer _renderer;
    private MaterialPropertyBlock _propertyBlock;

    private static readonly int VirtualMatrix = Shader.PropertyToID("_VirtualMatrix");
    private static readonly int TrueVp = Shader.PropertyToID("_TrueVP");
    private static readonly int TrueIvp = Shader.PropertyToID("_TrueIVP");

    // Start is called before the first frame update
    void Start()
    {
        _cam = Camera.main;
        _renderer = GetComponent<Renderer>();
    }

    // Update is called once per frame
    void Update()
    {
        if (_propertyBlock == null)
        {
            _propertyBlock = new MaterialPropertyBlock();
        }
        
        Matrix4x4 virtualMatrix = GL.GetGPUProjectionMatrix(_otherCam.projectionMatrix, true) * _otherCam.worldToCameraMatrix;
        Matrix4x4 inversCamProjection = GL.GetGPUProjectionMatrix(_otherCam.projectionMatrix, true).inverse;
        Matrix4x4 currentCW = _cam.cameraToWorldMatrix;
        Matrix4x4 currentWC = _cam.worldToCameraMatrix;
        
        Matrix4x4 VP = GL.GetGPUProjectionMatrix(_otherCam.projectionMatrix, true) * currentWC;
        Matrix4x4 IVP = currentCW * inversCamProjection;
        
        _renderer.GetPropertyBlock(_propertyBlock);
        
        _propertyBlock.SetMatrix(VirtualMatrix, virtualMatrix);
        _propertyBlock.SetMatrix(TrueVp, VP);
        _propertyBlock.SetMatrix(TrueIvp, IVP);
        
        _renderer.SetPropertyBlock(_propertyBlock);
    }
}

PerspectiveLockShader.shader

// Upgrade NOTE: replaced '_Object2World' with 'unity_ObjectToWorld'

// Upgrade NOTE: replaced 'mul(UNITY_MATRIX_MVP,*)' with 'UnityObjectToClipPos(*)'

Shader "Renovation/PerspectiveLockShader"
{
    Properties
    {
        _Color ("Color", Color) = (1,1,1,1)
        _MainTex ("Albedo (RGB)", 2D) = "white" {}
        _Glossiness ("Smoothness", Range(0,1)) = 0.5
        _Metallic ("Metallic", Range(0,1)) = 0.0
    }
    SubShader
    {
        Tags { "RenderType"="Opaque" }
        LOD 200

        CGPROGRAM
        // Physically based Standard lighting model, and enable shadows on all light types
        #pragma surface surf Standard fullforwardshadows vertex:vert

        // Use shader model 3.0 target, to get nicer looking lighting
        #pragma target 3.0
        
        #pragma enable_d3d11_debug_symbols

        sampler2D _MainTex;

        struct Input
        {
            float2 uv_MainTex;
            float multiplyValue;
        };

        half _Glossiness;
        half _Metallic;
        fixed4 _Color;
        fixed _Amount;
        
        float4x4 _VirtualMatrix;
        float4x4 _TrueVP;
        float4x4 _TrueIVP;

        // Add instancing support for this shader. You need to check 'Enable Instancing' on materials that use the shader.
        // See https://docs.unity3d.com/Manual/GPUInstancing.html for more information about instancing.
        // #pragma instancing_options assumeuniformscaling
        UNITY_INSTANCING_BUFFER_START(Props)
            // put more per-instance properties here
        UNITY_INSTANCING_BUFFER_END(Props)
        
        void vert(inout appdata_full v, out Input o) {
            float4 globalPos = mul(unity_ObjectToWorld, float4(v.vertex.xyz, 1));
            float4 globalPos0 = float4(globalPos.xy, 0, 1);
            float4 virtualClipPos = mul(_VirtualMatrix, globalPos);
            float4 virtualNormalClipPos = virtualClipPos / virtualClipPos.w;
            float4 virtualClipPos0 = mul(_VirtualMatrix, globalPos0);
            float4 virtualNormClipPos0 =  virtualClipPos0 / virtualClipPos0.w;
            float4 clipDistance = virtualNormalClipPos - virtualNormClipPos0;
            float4 clipPos0 = mul(_TrueVP, globalPos0);
            float4 normClipPos0 = clipPos0 / clipPos0.w;
            float perspectiveCoe = virtualClipPos0.w / clipPos0.w;
            float4 perspectiveClipDistance = clipDistance * perspectiveCoe;
            float4 normClipPos = normClipPos0 + perspectiveClipDistance;
            
            float a = mul(_TrueIVP._m20_m21_m23, float3(normClipPos.xy, 1));
            float b = mul(_TrueIVP._m30_m31_m33, float3(normClipPos.xy, 1));
            float w = (globalPos.z * _TrueIVP._m32 - _TrueIVP._m22) / (a * _TrueIVP._m32 - b * _TrueIVP._m22);
            float z = (1 - b * w) / _TrueIVP._m32 / w;
            float4 normClipPosFixed = float4(normClipPos.xy, z, 1);
            
            float4 clipPos = normClipPosFixed * w;
            float4 resGlobalPos = mul(_TrueIVP, clipPos);
            float4 resPos = mul(unity_WorldToObject, resGlobalPos);
            v.vertex.xyz = resPos;
            UNITY_INITIALIZE_OUTPUT(Input, o);
        }

        void surf (Input IN, inout SurfaceOutputStandard o)
        {
            // Albedo comes from a texture tinted by color
            fixed4 c = tex2D (_MainTex, IN.uv_MainTex) * _Color;
            o.Albedo = c.rgb;
            // Metallic and smoothness come from slider variables
            o.Metallic = _Metallic;
            o.Smoothness = _Glossiness;
            o.Alpha = c.a;
        }
        ENDCG
    }
    FallBack "Diffuse"
}