A trained eye that has seen both is the best answer. Also, the feel of antler is different than plastic. Antler, being a natural product, also has pores.
Take them off the gun. Heat up a needle and stick it in the back side. If they're real stag it'll smell like hair burning. If they're plastic, it'll melt a hole in it, but only a pin size hole.
Looking at pictures of knives for sale what jumps out at me first is plastic stag normally has bark that is too consistent. The real stuff usually is so irregular that I hunt through knives for sale for ones that have sides that are more symmetrical in shape than average and the bark on the two sides matches better than average. That's the goal anyway. With real stag you often have to settle for popcorn on one side contrasting with striations on the other or knarly bark on one side and fine striations on the other. If the match is great suspect plastic until you know otherwise.
Just take them off of the gun and look at the back. Stag will be flat and porous. Plastic will have pockets and reinforcing ribs. As a matter of fact you may not have to remove them from the gun. Just look at the bottom of the butt, along the frame you will probably see signs of the porous core of the antler. Fake will be smooth and solid.
There are some fake stag that are solid on the back, but they will still not appear to be porous. These ones are cast from a resin. Like the stocks in this post, Grip help they are obviously fake. See how easy that was!