Previously, I have done this (swapping between devices) many times, always formatting the SDXC card, after placing it in the new camera, just as a precaution. My experience comes from way back when I used to format my 1/4" floppy discs when using them in a different PC, as a way of making me feel that the disc is going to read/write ok, if the format worked smoothly.
Wrong reason, right action. With PCs, basically all of the PCs share the same operating system code and/or have it extensively tested for compatibility. The reason to reformat floppy disks is differences in head alignment. That's the same reason that on good quality tape drives, playback results are usually best using the same tape drive that you started with.
Now SDXC cards, as opposed to floppy disks, come with their own controller and talk only digitally/electrically to the camera/cardreader. There is nothing even remotely similar to the head alignment thing of magnetic media.
Instead, the problem may lie with a camera-internal operating system that implements the format in question in its own way, and there will be at best minuscule amount of testing involving third-party devices writing on the media.
Camera file data tends to be organized in a very straightforward manner for any given camera. If a camera takes stupid shortcuts (or has buggy code not working with all preexisting structures) like relying on some initial directory hierarchy being created in certain places on the medium or allocating new files in a different manner than standard on the file system, or is unhappy with file names looking significantly different from what it would create itself, having multiple devices (including cardreaders!) write to the medium in alternation can cause trouble.
This is even more likely with SDHC cards and earlier which use the FAT/VFAT file system (with the camera only needing FAT style file names but VFAT being often used by general purpose computers to allow for file names and directory hierarchies not supported by the original FAT). Or with early cameras supporting SDXC (it's not like the Exfat file system is so very old).
So while reformatting might take a hit on the read/write cycles of a card, it's a reasonable paranoia reason. Taken to some more extreme paranoia, you'd never edit, delete, or store anything on the card using a card reader (including the camera in mass-storage mode), making sure that only the camera is allowed to change the card.
I don't do that. And so far I've not been bitten by camera problems, the worst being some, uh, Casio? camera with xD memory cards putting on a file system crashing my (Linux) Laptop. That was irritating.