It depends on the synthetic material.
Natural (real) Tortoise Shell, Walrus Ivory, and Elephant Ivory, whale bone, (among many others), for example, unless pre 1910's(?) with documentation to prove it upon demand, is banned, illegal to possess, and subject to seizure.
The synthetic imitations are legal, and look identical. (some look so identical they have to be viewed under a black light to confirm they are a synthetic, and not real).
I like the look of tortoise shell and ivory on some knife patterns.
As much as I would like a knife with real Ivory, tortoise shell, or whatever, I have less than zero desire to carry around a briefcase or backpack containing the several pounds or reams of documentation tracing the ownership of the material from when it was collected, perhaps in the 1700's or before, telling who shot the critter and when, down to the minute, his or her hunting license number (possibly requiring a copy of that license), the names of the safari guides and porters, used, etc., along with the names of everyone who owned it before it came into my possession.
I heard that CITIES is debating banning fossilized Mastodon Ivory and all other Mastodon parts (so what if mastodons been extinct for around 40,000 years?) along with fossilized walrus, whale and dinosaur parts.
Synthetics are the only practical way to have "tortoise shell" and "Ivory" (and possibly in the near future fossilized Mastodon and other critter parts)
Synthetic Abalone, and other sea shells, Pearls, corals, etc. (not banned by CITIES), are much more affordable than the genuine article, as well.
The only synthetic covers I own are acrylic (one Rough Rider Barlow with imitation Abalone, and clear (over artwork), on four Rough Ryder "Rider's of the Silver Screen" moose), smooth G10, smooth black canvas micarta, and Delrin/Stagalon.
I don't object to how they feel in hand.
I will admit I'm not overly fond of how two of the three knives I have with Stagalon look. (nowhere close to real stag.)
The only natural cover materials I own are wood, (some "stabilized" (why?) by filling with epoxy or whatever, some unstabilized) bovine bone, stag, and (naturally dropped) elk antler.