No, it isn't. It is influential, not authoritative.
And, in this instance, it is outdated.
Common usage, which you can see as easily as I can. For example, do news agencies typically use FBI or F.B.I.? Do they typically use UN or U.N.?
> That is, what is the evidence that current professional editors are on record as saying that the quoted advice is old-fashioned and not to be regarded?
You again misunderstand the role professional editors (and, by extension, style guides) fill. They enforce what's commonly known as a 'house style', which may be influential outside of a given 'house' (company or newsroom) but is not authoritative in any sense anywhere but that single location. Language is not defined by books: it is described by them.
> (This subthread started, after all, with an HN participant noting that editors were FOLLOWING the quoted rule.)
That comment was deleted before I got to it.
"7.16 Use of apostrophe
"To avoid confusion, lowercase letters and abbreviations with two or more interior periods or with both capital and lowercase letters form the plural with an apostrophe and an s. See also 7.63-65."
The term "G.P.A." has two or more interior periods, and that is why the apostrophe appears before the letter s that forms the plural of that term.
There is an online version of the Chicago Manual of Style, which you may or may not find behind a paywall depending on what subscriptions you have.