Should you no index account, login, and registration pages?

no index account pages

In general, yes. There is not much value in indexing pages related to account management (including password reset pages).

As such, we would generally apply a noindex on them for good measure. You are making a business decision and choosing to eliminate that page from appearing in your sitelinks from what I would presume to be a top-level navigational page.

That said, there is a scenario wherein it may make sense to keep them so they are more easily surfaced when your users perform Navigational searches – for example, Googling facebook login will yield as the top result.

This is because the best page to meet that specific search query and the intent is the log in page for Facebook.

There is also specific Item Types such as that specifically refer to this user action. It may also be a useful signal to Google that your website involves interaction which will help classify the type of website and webpages it contains.

As long as these pages aren’t one that could affect crawl budget (depending on your setup), we see no harm in including these pages in SERPs (by not marking them as noindex).