It's a spelling error (for those who believe in such things).
Its use is negotiable with numbers, acronyms, and other abbreviations.
Even then, it's never necessary. A total prohibition against it is never wrong and is easy to remember. Hooray!
This article satisfies Squid Commo Objective #3: Clarify and simplify the rules.
What do queue, colonel, indict, auxiliary, and Favre all have in common? They look misspelled, but they are absolutely spelled correctly. If you spelled them any other way in a competition, you would get ejected. And rightly so. Likewise, this practice of rewriting weird-looking plurals like dos, don'ts, yeses, and noes as do's, don't's, yes's, and no's will get you sent home from the spelling bee. And rightly so.*
I advise my students to never use an apostrophe to form a plural, no matter how dorky it may appear without it (which is why we started the practice). Yes, the plural dos looks like the acronym DOS (disk operating system), but that was never a problem before the 1980s. (It may not be a problem now, except for us old farts who remember DOS.)
I don't believe that we should reroute the highway of correct spelling every time someone, anyone, erects a new acronym.
Besides, adding apostrophes to words willy-nilly takes us down the slippery slope to Evendorkierwordstown, like when we change don'ts to don't's. That's not an improvement by anyone's standard.
But there exists an area of editorial indulgence when it comes to numbers and abbreviations, especially acronyms.
Until the double apostrophe shows up.
For example, one of my all-time favorites, Kurt Vonnegut, would form a year's plural by adding an apostrophe and an s after it, e.g., 1960's, and it would pass editorial muster. (Actually, Vonnegut did it both ways, with and without the apostrophe. It may have been an editor's call on that.)
But when a possessive is added to the number, you get this clumsy double-apostrophe action going, which no one thinks is appropriate.
The Beatles were the 1960's' top-selling artists. If you contract the year, it gets worse: The Beatles were the '60's' top-selling artists.
The NCO's' parking lot is closed.
So I'd rather you not do that.
For me, the advice "don't use an apostrophe to form a plural" is sound because it's easy to remember and is never wrong.** You don't have to remember rules about when you use the apostrophe for plurals and when you don't, and you avoid the inevitable confusion that leads you to use apostrophes when it is clearly wrong.
But in the end, using it with numbers (e.g., 1960's) and acronyms (e.g., NCO's) doesn't distract the reader or otherwise hamper the communication. Sometimes, I suppose, with acronyms, it could make it easier to read as a plural, e.g., "How many ISS's are there?"*** So I don't count off for it. Just be careful you don't try to add possessives to them.
I would, however, thump you for its use on every other sort of word, especially contractions like don't's. That's harmful to all vertebrate life forms.
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* Merriam-Webster lists do's as an alternative to dos, and Collins lists no's as an alternative to noes. But wait until you get back from your first field trip before you bring the smack down on me.** Yes, it's true. The apostrophe is probably necessary when you're referring to certain mathematical variables like x's and y's. But no one is going to argue that conventions of mathematical notation should dictate PUG. Not without getting claqued.*** Actually, I'd probably write it as ISSes.