The gestalt rules come from Unearthed Arcana, a collection of open-content variant ideas that Wizards of the Coast threw together and called a book. Some of them were written by Wizards of the Coast staff, others were published elsewhere as open content, and so on. Most importantly, they are often closer to ideas for how to vary your game, than they are fully-fledged and edited rules. That means they always require some DM judgment and adjudication to implement, because they are ultimately not always complete.
For example, the gestalt rules never explain how to handle RHD and LA. It’s not clear that those should go on “one side” as you have done—I have played in games that have ruled that LA is applied “before” the entire gestalt business, so it adjusts both sides. In my own games, I just ban RHD and LA altogether, in general, but also particularly for gestalt—neither ruling suits me.
I have also played in games that banned swapping which side a class is on. No rule says that, though the reasoning behind dual-advancement prestige classes might be generalized to make an argument in favor of such a ban. But this is part and parcel of the process of implementing a variant idea: the DM has to massage the ideas that Unearthed Arcana presents into something that is actually a fully realized and implemented rule. That can include a ruling like this.
Now, if it’s a fellow player making this proclamation, they may have simply gotten the wrong impression that this is “an official rule” from a ruling from some other DM in some other game. In such a case, it may be worthwhile to check with this DM for this game. And maybe there’s some room for push-back even if it is the DM, if they are under the impression this is “the rule” and that’s the only reason they’re implementing it.
Personally, though, I think it is best to not see gestalt as “sides,” because that’s not really what the rules describe. You don’t really have one side of LA +1/6 RHD/+2 warshaper and another side of 4th-level warblade/3rd-level warshaper/+2 warblade. What you actually have here is a level of LA//warblade, then three levels of RHD//warblade, then three levels of RHD//warshaper, and finally two levels of warblade//warshaper. This matches the way the actual gestalt rules are worded, where it describes how you combine two classes together to form a single level. And since neither class in a gestalt is in any way “primary,” it’s clear that a warblade//warshaper and a warshaper//warblade are the same thing. In this sense, there isn’t really any “swap” going on in the first place.
Which works out to being the same as “allowing” the “swap,” and since you usually tabulate gestalt characters’ levels so you can try to keep track of your class level in each, the “swap” will appear to be in the table. But I think seeing that the “swap” really isn’t any such thing motivates the idea that there should be no reason to bar it. And while I have played in games that banned the “swap,” I have played in many more than have not—and I have never seen it cause a problem. Indeed, since the “swap” isn’t really any such thing, it seems pretty clear that it cannot cause problems.
You can run into difficulty if you make a ruling like
you can take mystic theurge levels so long as you get the requisite spells entirely on one “side,” so that a 7th-level whatever//3rd-level cleric/3rd-level wizard/1st-level mystic theurge is allowed, but a 3rd-level cleric/1st-level whatever//3rd-level wizard/1st-level mystic theurge is not.
but notice that this is not a part of the rules as Unearthed Arcana describes them. It’s an entirely-reasonable houserule, but as-written Unearthed Arcana just bans mystic theurge and other prestige classes like it for gestalt games. When you introduce changes like this, it can cause weird corner cases. Suddenly, “sides” are actual things, and “swaps” could potentially make a difference (though again, in my experience they never have—and we usually use a rule like this—and frankly I’m not seeing any way a swap could cause problems).
But seriously, your ruling on RHD and LA is vastly more likely to cause problems than this is. In fact, while I literally cannot see any way a “swap” can cause problems, in my experience, RHD and LA are all-but-guaranteed to cause problems.
