I hope that someone here can help me settle a discussion between fellow riders.

Assuming there is no change in the fore/aft position of a saddle, will the use of a setback or zero setback seatpost make any difference? Some of us argue that no, since the position of the saddle does not change...

The main reason would be to get the saddle centered on the rails.

technically...yes.
1. Weight difference. Zero offset post will be lighter.
2. Dampening. Offset post should provide a softer ride.

Realistically? Nothing you can feel.

No real difference. Use the one which provides best saddle positioning.

assuming the same fore-aft and height, then there'd be no difference there.
But there would be in how all might function - if you're in the middle of the saddle rails on a 25mm setback post then you might not get back far enough on a zero - depending on the saddle rails - in the smilar situaton the adjustment will certainly be very limited in one direction, and if you wanted to try a different fore-aft, you might not be able.
If you do get back far enough then there is likelyhood that your leg might rub the post parts - depending on the post. Or the zero post might cause flaring of the saddle if it has skirts, and again, leg rubbing if it doesn't. Or a saddlebag or saddlebag attachment (as in velcro) might catch your legs/shorts and cause the dreaded 'leg fuzz' or worse, a hole.
Most road bikes come with some type of setback post, because for the avg rider with avg body dimensions, a setback gives adjustment both ways... but zeros do work well for many who try them... no black or white here

If you're looking for increased reliability or comfort then it may make a difference, depending on where your saddle is on the post.

If you already max out the saddle in a particular direction (say it's totally pushed back on a zero setback post) then getting a setback post will put the load in the center of the rails, not at one end. This could improve reliability, especially for those rails that actually say "No" at either end of the rails.

If you get a setback post it could be much more shock absorbent. VeloNews did a test measuring deflection/comfort and found certain posts to be much more forgiving than others. I don't remember specifics but I think all the comfortable posts were setback posts.

Therefore if you're looking to improve comfort at the back of the bike then a setback post may improve that.

I went from a straight post to a Vibe7 PRO setback post and was pretty shocked by the increased damping. It made a huge increase in comfort.

I like a particular set back of the saddle from the bottom bracket. If the frame has a steeper sta, or is bigger, I'll use a zero. If the frame is smaller or shallower, than a setback will be required.

As pointed out in the above posts, it's immaterial with respect to fit. Depending on relative characteristics of the parts it may affect ride quality.