Thank you for your answer.
What is "an alpha problem" and how can it be avoided?
To the untextured shape: I'm not using anti-aliasing. From what I understood from internet, there could be a rounding error of floats in the positions of vertices, but mine seem to be fine to me.
I also didn't mention that I'm rendering contents of a window (both texture and white box) into a RenderTexture, and only then I'm rendering that onto the background rectangle shape in the window.
I'd like to provide a minimal example, but when I tried to reproduce this problem with a new application, it wasn't there.
EDIT:Ok, I did a bit of further "testing".
I found that those borders aren't there if I overlap two RectangleShapes of the same color.
I am now sure that the problem is in the RenderTexture step. Notice that the characters here are not blured, because I rendered the box directly into the RenderWindow.
EDIT2: SOLVED!My RenderTexture´s IntRect was smaller (or different) than the size of the texture. That's it.