if you look closely there is a one pixel wide gap between the corners of the turtles and between the frame of a monitor and the screen. Moving closer ingame does not do anything since the line remains one pixel wide.

I think this is something with your GPU drivers, it used to do that on my friend's Minecraft, and it doesn't only happens on turtles or monitors.

i tested this with many vanilla blocks and it did not happen there...

This is just a floating point accuracy issue, can't do much about it.