Yes—generally it is safe to use the same SD card in different cameras. There is no solid technical basis for the claim that swapping cards between cameras by itself causes corruption or dramatically shortens card life.

Most cameras use standard FAT-based filesystems, which are simple and widely supported. Different cameras may create different folder structures, but formatting the card in the camera before use is a sensible practice and helps avoid compatibility or directory-layout issues.

Flash memory does have a finite write lifespan, but SD cards use wear leveling to spread writes across the card. Normal use across different cameras does not meaningfully change this. What matters is how much writing is done, not which camera does it. A full/low-level format writes more than simply shooting and deleting files, but even then card endurance is typically high enough that this is not a practical concern for normal photography use.

So: swapping cards is fine, and formatting in-camera before important use is good practice. Dedicated cards per camera may still be convenient, but not because sharing them is inherently harmful.