By default Valentina uses path /usr/share/valentina for standard tables and templates. On Unix systems path /usr is read only for common users. The issue occurs when file format version should be converted to new version. This process require write rights. As the result users see error: Permission denied.
I propose on start Valentina create folder .valentina inside a home folder (if doesn't exist already) and copy whole folder tree. Instead of files use symlinks.
If the app needs rewrite file, it checks if a file is symlink and we really have no write rights and copy real file to symlink folder. In our case .valentina inside a home folder. This is close to copy-on-write approach.