New Tab pages are already protected and cannot be auto-closed by the extension. Both about:newtab (Firefox) and chrome://newtab/ (Chrome) are excluded from duplicate detection before any comparison or whitelist logic runs. The "" entry would have no effect since the whitelist only applies to regular HTTP(S) URLs.

If you are seeing new tabs being closed, it is possible you have a custom new tab extension that replaces the default page with a regular URL. In that case, adding that URL to the whitelist would work. If this is still happening with the current version of the extension, please open an issue at https://github.com/Peuj/duplicate-tabs-closer/issues with more details.