The answer to your question is that there will always be some files changing during a backup, but most will be log files which don’t matter. Shutting down mediacenter will ensure Kodi’s database is kept intact and I have tvheadend which similarly ought to be stopped. If other machines might access and write to your RPi then you might want to shut down networking (connman.service) (unless you are backing up to a network share!) OSMC itself may check for updates at any time (if you have it set to auto-update).
Only you will know about any other things you might be running which are not part of OSMC.
raspiBackup is an interesting solution but from a quick look it seems to be missing some features that I built into this. You may like to try it if you are not going to want dd or tar backups. It doesn’t hold your hand as much as raspiBackup.