(Why are you expecting apparent sizes to match real sizes in the first place? The Sun looks as small as the Moon as seen from Earth, do you think it actually is?)
Of all light rays entering your eye right now, the ones coming from parts of the object farther away from you departed earlier than the ones coming from parts closer to you. If the object moved between those two times, its image will be deformed in a way that, when combined with Lorentz contraction, foreshortening, etc., will make the object look the same size as if it was stationary but rotated. This is known as Terrell rotation and there are animated illustrations of it on the Web.
(BTW, galaxies are moving along the line of sight, so their Lorentz contraction would be along the line of sight too, and how would you expect to tell (say) a sphere from an oblate spheroid seen flat face-first?)
I agree that “Lorentz contraction” is a misleading name; it's just a geometrical effect akin to the fact that a slab is thicker if you transverse it at an angle than if you transverse it perpendicularly.
will make the object look the same size as if it was stationary but rotated
Yes. Rotated rope looks shorter. Problem remains.
galaxies are moving along the line of sight
We see the close and the far edge of many of them. Still, the pancake apparently isn't neither squeezed neither rotated.
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.