Why is Alpha Cutoff Shader affected by glow?

My player character uses an Alpha-Cutoff-Diffuse shader to render, and the glow from the Image Effects/Glow is getting drawn on top of the player character.

Is there a way to alter the Alpha-Cutoff shader so that the glow won’t show through it?

Shader "Custom/Alpha Cut Off"
{
	Properties
	{
		_MainTex ("Base (RGB) Trans (A)", 2D) = "white" {}
		_Cutoff ("Alpha cutoff", Range(0,1)) = 0.5
	}

	SubShader
	{
		Tags {"Queue"="AlphaTest" "IgnoreProjector"="True" "RenderType"="TransparentCutout"}
		LOD 200
		
		CGPROGRAM
		#pragma surface surf Lambert alphatest:_Cutoff

		sampler2D _MainTex;

		struct Input
		{
			float2 uv_MainTex;
		};

		void surf (Input IN, inout SurfaceOutput o)
		{
			fixed4 c = tex2D(_MainTex, IN.uv_MainTex);
			o.Albedo = c.rgb;
			o.Alpha = c.a;
		}
		ENDCG
	}

	Fallback "Transparent/Cutout/VertexLit"
}

[4802-glow+through.jpg|4802]

I believe it is because the glow effect uses the alpha channel to deter-main where it should blur and increase the brightness:
http://docs.unity3d.com/Documentation/Components/script-GlowEffect.html

You could try using a modified version that this guy on the forums did:
http://forum.unity3d.com/threads/13107-Glow-effect-with-adjustable-threshold-(enjoy)

Finally found the answer to this one. The alpha has to be set to zero, or else the object glows, but if the alpha is set to zero, you see nothing n screen… unless you use the right blend mode!

Blend One Zero
color.a = 0;