RenderTexture transparency artifacts

I have a set up of two cameras. One of which is rendering to a texture ("Input") and the other one is rendering to the screen ("Output"). I am mapping the render texture that the Input produces onto a plane. The problem arises when I try to make the plane transparent by using the transparency produced by the Input Camera, using e.g. the default "Unlit/Transparent" shader.

In order to gain a transparent output from the Input camera, I have to resort to setting the clear flag to either solid color or skybox and choose a fully transparent color of type (_,_,_,0).

However, as you can see in the image, this introduces bad artifacts. Are there any ways of working around this or alternative avenues I could explore?