They are until the bullet leaves the barrel. After that the earth and the bullet are no longer connected so there is no force exerted on the bullet at that level. It happens to everything not attached to the earth. Newton says the effect of momentum will drop off unless there is a force applied. The impact will be to the right in the Northern Hemisphere if you are shooting north. This is a proven effect not a theory.The bullet has momentum given to it by the turning of the earth while it's in the gun. It doesn't loose the momentum just because it leaves the barrel. The gun is rotating with the earth and has no force working on it that is different from the bullet since the gun's momentum is continuous, as is the bullet's. And the air is also rotating with the earth, so it does not put any extra force onto the bullet relative to its momentum other than that created by weather. This is a non-issue. Other things must be in play, but not the rotation of the earth.
Another way to say it is that the earth, the gun, the bullet, and the air all are rotating together.
Oh, and as a nifty treat, east west does affect a impact. Firing due east you will impact low, west high. There are some who say that a head wind or tail wind doesnt have an effect. However they do. A headwind will cause the impact to be low and a tailwind will cause the impact to be high of your no wind zero. basically the bullet has to travel through more air in a headwind "farther" if you will and like a jet that picks up a tailwind, the bullet travels "faster". You can see that at mid range.
Long Range Shooting: External Ballistics - The Coriolis Effect
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The thing is though, on a known course, the same course, the affect should be null after establishing a no wind zero. East West North or south. Once you get a zero for that range, rifle and ammo, you are good to go. At 1000 yards you are looking at under 4 inches, which is enough to miss if you make any other calls poorly. Good luck getting a no wind zero over 4.4 miles though.