With my research I have found that using a VBO to render graphics is much faster than using depreciated OpenGL. I've found with this that you can't switch textures mid VBO render, so if I have multiple objects in a single VBO, they all have to use the same texture. I solved this problem by using a texture atlas to combine multiple textures together into one texture used throughout the whole VBO.
Now all this works perfectly. It's fast, it's efficient, and it looks good until you turn on SFML's anti-aliasing. If you look at the pictures, it appears that it's merging textures in the texture atlas at a distance. These pictures should help clear up what that means.
The Atlas Map as it looks in memory:
Also if it helps, I experimented with adding blank space between these individual textures to see if that would hide the problem. The problem persists, only it makes objects far away appear translucent because of the alpha between the textures.