They probably aren’t in the whitelist because nobody has gotten round to adding them yet. There is a ticket for Mudcat, but not yet for the Digital Tradition Folk Music Database. You can add your vote to the existing ticket and create a new one for the other database.
Of course, talking about it here does increase your chances of getting them included earlier.
MudCat Café (and by extension the(ir) “DT”) is a site that I used to be involved with, so I know them somewhat. However, to the best of my knowledge, they don’t have a license and they also publish lyrics that are not in the public domain, so they’re (unfortunately) not a safe lyrics link. It might be a good “other database” target though, since they do have a wealth of information about traditional/folk(-ish) songs.
Being reasonably linkable, I guess. Preferably with an identifier as part of the URL, but not necessarily.
Also, for things such as “The Roud Folk Song and Broadside Index”, Child Ballads, etc., we would ideally have as close to an official source for this, if there’s a university or foundation or something that maintains such a thing.