Render Texture from Cameras targetTexture produces seams.

I am attempting to render a specific section of my scene using a separate camera, and a render texture. That object is on a separate layer that the main camera is not rendering, but a separate camera is. The secondary camera has a target texture set to be a render texture that I have created. Everything is working as intended except for the fact that the object, when rendered to a texture, has a bunch of seams that are not present when rendering directly to the screen.

What it looks like when rendered directly to the screen:

What it looks like when rendered to a texture, and then displayed on a quad in the scene:

Notice how the second image has a bunch of transparent "lines" in between the sprites where there shouldn't be any.

I am using a basic transparent shader to display the render texture on the quad (since the background isn't part of the render texture, just the black crowd part). I have tried a number of different shaders, and none of them seem to make a difference.

The render texture's settings are: Width: Screen.width Height: Screen.height Format: RenderTextureFormat.ARGBFloat;

Unity Version: 5.2.3f1 - iOS Platform

Edit: The reason I am doing this is so that I can apply a "Blur" image effect to the texture, and make the crowd in the foreground appear to be out of focus. Any alternative suggestions for how to do this are also welcome.