Your surgeon is the one who knows exactly what he/she did in your operation, so listen carefully to that advice. If both the head of the femur and the acetabulum were replaced (which sounds like your case), you have the situation where metal on metal stress is occurring. Inanimate materials are not self-healing. If you stress these too much, they will wear out more quickly. However, if only the femoral head was replaced, then you still have a bony acetabulum with, presumably, some cartilage. Living tissue require stress to remain healthy, but too much stress will lead to degeneration.
Depending on what was done, you may have to drastically limit certain movements to avoid wearing out inanimate material or to find some threshold of movement that can stimulate animate/living tissues without going too far and wearing them away. I can see why your surgeon doesn’t want you to go to your end range of motion. But to have no movement is also not great. See my article on Antifragility
: we need to stress living tissues to stay healthy, but when we are injured the distance between too much stress and too little stress is very short. You can easily do too much, but you need to do something.
Normally, external rotation and abduction are okay for people with hip replacement, but adduction and internal rotation are not great. Shoelace is extreme adduction, so I can see why that is forbidden to you. Square pose may come back to you in time, but what’s the hurry? For now, stick to Butterfly, or try wide Square (knees wider than hip-width apart.) In your case, you are also being warned not to do so much extension or flexion either. This may be because many of the capsular ligaments that prevent too much extension were damaged or removed in your operation. Deeper flexion may be possible/available if accompanied by external rotation and abduction (ie: have your legs a bit wider apart and slightly externally rotated when you flex at the hips and see how that feels.) Again, I would listen to your surgeon and not go too deeply in these directions.
Part of your current lack of ROM may be some lingering inflammation, which should diminish in time, if you let the area heal. If you keep pushing to your edge, that inflammation may remain for longer. So, again, back off and find what your appropriate edge is today. (Another way to reduce chronic inflammation is earthing. Check out this article
As a yoga teacher, you are a pioneer, whether you like it or not. What you are learning will be very valuable to others about to face what you are experiencing. Please let us know how your journey goes!