Transparent shader: final alpha value wrong

I'm currently working on a cloud system which shows near clouds as meshes and far clouds rendered into a skybox. The problem is, that the clouds being rendered to the RenderTexture have a different alpha value.

This is how a cloud looks like when being rendered to the screen:

I would expect the alpha channel to look something like the rendered cloud but it's not:

This is the shader I'm using:

 Shader "Custom/CloudShader"
 {
     Properties
     {
         _MainTex("Base (A)", 2D) = "white" {}
         _Color ("Color", Color) = (1.0, 1.0, 1.0, 1.0)
     }
     
     SubShader
     {
         Tags { "RenderType" = "Transparent" "Queue" = "Transparent" }
         Blend SrcAlpha OneMinusSrcAlpha
         Cull Off
         ZWrite Off
         LOD 200
  
         CGPROGRAM
         #pragma surface surf NoLighting
         
         fixed4 LightingNoLighting(SurfaceOutput s, fixed3 lightDir, fixed atten)
         {
             fixed4 c;
             c.rgb = s.Albedo; 
             c.a = s.Alpha;
             return c;
         }
         
         
         uniform sampler _MainTex;
         uniform fixed4 _Color;
  
         struct Input
         {
             float2 uv_MainTex;
             float3 viewDir;
             float4 color : COLOR;
             float3 worldPos;
         };
  
         void surf (Input IN, inout SurfaceOutput o)
         {
             const float FADEOUT = 20;
             float dist = distance(_WorldSpaceCameraPos, IN.worldPos);
             float factor = saturate(dist / FADEOUT);
         
             o.Albedo = _Color.rgb * IN.color;
             o.Alpha = _Color.a * tex2D (_MainTex, IN.uv_MainTex).a;
             
             o.Alpha *= factor * saturate(abs(dot(o.Normal, normalize(IN.viewDir))) - 0.3);            
         }
         ENDCG
     } 
     FallBack "Diffuse"
 }
     

It seems the alpha value rendered to the RenderTexture is different from the value on the screen. What would I have to do to get the same results?

(Using the grayscale for the alpha channel doesn't give me a correct result.)