When it comes to SEO, password protection like this means that Google and other search engines won't be able to index it either.
Because Plug in SEO views your shop just like a search engine does, this also means that we can't check a password protected store.
What a lot of shop owners do is:
- temporarily remove the storefront password
- run the Plug in SEO check they're interested in, pushing the refresh icon to make sure to fetch the latest version
- fix any issues flagged by Plug in SEO
- re-add the storefront password
Or some unlaunched shops simply remove the password altogether as they haven't promoted their shop yet and won't get any customers stumbling on it.