My shader brakes depth of field

Hi Community! I have a scene where I really need depth of field.

Apparently, Unity's depth of field doesn't work with any of the shaders, neither built-in or custom, that process the alpha.

So this happens, for example, with the Transparent/Diffuse shader. Transparent/Cutout works instead.

Here's the simplest custom shader I made that triggers this behaviour:

 Shader "Custom/SimpleAlpha" {
     Properties {
         _MainTex ("Base (RGBA)", 2D) = "white" {}
     }
     SubShader {
         Tags { "RenderType"="Transparent" "Queue"="Transparent" }
         //Tags { "RenderType"="Opaque" }
         LOD 300
         
         ZWrite Off
         
         CGPROGRAM
         #pragma surface surf Lambert alpha
         #include "UnityCG.cginc"
 
         sampler2D _MainTex;
 
         struct Input {
             float2 uv_MainTex;
         };
 
         void surf (Input IN, inout SurfaceOutput o) {
             half4 c = tex2D (_MainTex, IN.uv_MainTex);
             o.Albedo = c.rgb;
             o.Alpha = c.a;
         }
         ENDCG
     } 
     FallBack "Diffuse"
 }

If you try the code in a project you'll notice that EVERY object that wears the shader is blurred with the very same amount instead of being blurred basing on Z. I already tried to turn ZWrite On but the result is the same.

Any help is much appreciated. Thanks in advance.