Short answer is: yes, as soon as more than one OS mounts a file system in read-write mode.

The kernel of a modern OS (I am generously including Windows here) caches file system data structures in memory. When you hibernate the computer, the content of that memory is written into a large file because that speeds-up a later restart.

Now, if you boot up another OS, and modify these partitions (without mounting them read-only), you alter the file systems data structures. That happens already when you view folders because this modifies access times stored in the inodes.

When you now shut down the second OS, and resume the first OS, the restarted kernel will have and use cached file system metadata which id loaded from the image into the kernel, that does not match that of the files on disk. And this causes file system corruption by definition.

I wrote a quick guide on using Puppy Linux with Ventoy, so you can put a Linux install on your keyring and get a consistent environment across different systems. I found Puppy is much easier to get working than Slax for persistent data storage. Hope it's helpful to someone. 😀

.... virtual machines where you only have to select which accompanying image of Arch / Tumbleweed / Ubuntu / Fedora you want to try.

In addition, the combination of a very stable base system with a fast-moving, bleeading edge virtualized system on top can be surprisingly useful. And because small virtual machines, when not running, are nothing else than files on your computer, you can have many versions of them, alter things, try stuff out, then delete it and go back to the tidy original state.