Yes, reinstalling macOS under these circumstances1 may erase app data.
If you don't have a Time Machine backup (and you really really should), then the other options you have are:
- export your bookmarks from Firefox as a html file
- export your bookmarks from Chrome as a html file
- ensure your Notes files are synced to iCloud
You would then just copy the HTML files you exported onto an external USB drive for importing back later, and your Notes files will be available to your other Apple devices (or via the web) assuming you have other Apple devices with iCloud enabled.
Finally, you could also use Chrome's and Firefox's built-in syncing services to save your bookmarks.
NOTE: If you don't use iCloud, you could always just copy and paste your Notes into another app from which you can save them onto an external disk (e.g. TextEdit, Pages, MS Word, etc).
1 It's unclear what you mean by 'disk errors', but if these are such that your startup volume needs reformatting then your data will be lost.