TargetTalk

When shooting a rifle righthanded, your left side faces the target.
If you sway forward, you and the point of impact will move to the right.
Long experience has taught you to compensate using the muscles of your legs etc. to keep your balance. The pressure under your feet also gives feedback telling you what's going on.

A righthanded pistol shooter faces the other way and when leaning forward, will move to the left in relation to the sight line.
Now all the body reflexes work the other way around. The feedback from your feet etc. is the same as before, but you will be looking over your right shoulder and the visual feedback is the opposite.

What to do if shooting both rifle and pistol?
Favour one discipline over the other when it comes to amount of training?
Start shooting lefthanded pistol to keep systems consistent?

Is this an old thing that's been discussed before?

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Firstly your body should be balanced so that as far as possible the weight is distributed over both feet evenly. Secondly you can train for both (standing) rifle and pistol, but because they are so different the direct training totally different. You really need to decide whether you want to specialise in one, and do the other as more of change, or generalise and do both, but knowing that you are unlikely to attain the same peak of performance. I kind of do the former concentrating on pistol and training that, and I shoot prone rifle more for a change.

Rob.

I agree that the two are so different it shouldn't matter much so long as you're concentrating. While shooting in college, a number of people said I shouldn't shoot skeet at the same time due to the trigger pull. The only time skeet came to my head with rifle was Perry this summer and the crazy winds, but It was more of a joke in my head than a change in strategy.

I also agree that you can't attain you peek performance in both at the same time, but not due to the disciplines being different. It would be due to you splitting practice time. Once you get past a certain baseline level in a sport, you have developed fundamental processes to use.

Take me in tennis and golf. I work as a tennis pro, so that is the more engrained sport. Therefore, I love to put topspin on the ball. That translates to a really bad hook in golf. That's what my golf games looked like to begin with, the ball taking a very deliberate left turn 50 yards off the tee. My tennis processes were the closest muscle memory I had to a golf swing.

With some practice, I straightened that hook out. I learned what a golf swing should be like to hit the ball straight (relatively). Now I have a whole new set of problems to deal with in a whole other sport. But none of those have translated back to my tennis game in any way.