A 1.4x extender will decrease your maximum aperture by 1 stop. A 2x extender will decrease your maximum aperture by 2 stops. Canon claims AF speed reduction of 50% with a 1.4x and 75% with a 2x extender. All extenders decrease the contrast of your image. All extenders soften your image, particularly at wider apertures.
This Smugmug gallery has 5 shots I took of the moon last May using an EF 800 f5.6 bare, with a 1.4x, a couple with a 2X, and the last with a Celestron CPC 1100 (equivalent to a 2800mm f10 lens) using a 1DX III. The lens data for each image is available in the information button, the telescope shows
For example, the excellent EF 70-300L lens is not compatible either. The EF 75-300 lens won't work either and it's optics are woeful to begin with: it would just get that much worse with an extender added if it was physically possible. The extenders are selective on which bodies they will work with too: only a few, recently released bodies will
The range of Canon 1.4x and 2x lens extenders. The teleconverters (TC) will multiply the focal length of any EF lens used with them by either 1.4x or 2x. So, a 300mm lens beomes a 420mm with a 1.4x TC and a 600mm lens with a 2x TC. KSh7.