I finally fixed it! By using the following command I found out, that in the render loop we don't render to framebuffer object 0, but a diffrent one.
GL11.glGetInteger(EXTFramebufferObject.GL_FRAMEBUFFER_BINDING_EXT);
Now before I create the framebuffer or bind it get the "default" id that in need to switch back to when I am finished. This fixes the issue.
Now i just have to figure out why the drawn texture is not working as expected...