Shady password required for Update Apple ID Settings My iPhone (under iOS 12.1) informs me that I should "Update Apple ID Settings" for otherwise "Some account services will not be available until [I] sign in again." 

When I launch Settings > Update Apple ID Settings iOS first promts me for my "Apple ID Password", then "iPhone Passcode", and then "Mac Password". The description for the last one reads: "Enter the password you use to unlock the Mac ...". 

What password does this refer to? I hesitate to type in lots of passwords without better information on what's going on here. I do own both an iPhone and a MacBook and use the same Apple ID account on both.
You should ignore this and click cancel. This screen is an undocumented part of Apple's security practices (i.e. they don't mention it in their own documentation anywhere) and it exposes you to the risk that Apple will store, or could compromise (possibly resulting from a warrant/writ) your password for your local device.

This is documented further here https://privacylog.blogspot.com/2019/05/security-flaws-with-apples-two-factor.html