These relate to physics/modeling. I am going to hand wave a bunch.

If a system has to operate the same way under rotation/reflection, that strongly constrains what the system can be doing. Think crystals or isotropic forces or, in the day job, what should happen if you negate a feature going into a neutral network then retrain. Should it matter from which perspective you look at a thing?

If a system is continuous then smooth changes to inputs should cause smooth changes to outputs. The system probably will be robust to small perturbations because they will result in small output changes.

https://en.m.wikipedia.org/wiki/Turbulence#Kolmogorov.27s_th... is something of an example.

Not the author of the comment, but I can give an example of how it's used in physics. The first law of thermodynamics states (in a simplified form) that the energy into a system is equal to the energy out. So it's a symmetrical process. This means a lot of times we can calculate half of a thermodynamic process, (i.e the heat flow into a system), and know that, over a long enough period of time, the heat flow out of the system will be equivalent.

Consider conservation of energy and momentum. Of course, one should operate within the limits of thermodynamics too.

Not OP, but I view this as a special case of "form over function"