Plurals of acronyms, letters, numbers — use an apostrophe or not?

I seem to remember the old askoxford.com site said either was acceptable: CDs and CD's.

But now the replacement Lexico powered by Oxford firmly suggests to avoid the apostrophe except in a few special cases:

Apostrophes and plural forms

The general rule is that you should not use an apostrophe to form the plurals of nouns, abbreviations, or dates made up of numbers: just add -s (or -es, if the noun in question forms its plural with - es). For example:

...
MP MPs (e.g. Local MPs are divided on this issue.)

1990 1990s (e.g. The situation was different in the 1990s.)

It's very important to remember this grammatical rule.

There are one or two cases in which it is acceptable to use an apostrophe to form a plural, purely for the sake of clarity:

• you can use an apostrophe to show the plurals of single letters:
  • I've dotted the i's and crossed the t's.
  • Find all the p's in appear.
• you can use an apostrophe to show the plurals of single numbers:
  • Find all the number 7’s.

These are the only cases in which it is generally considered acceptable to use an apostrophe to form plurals: remember that an apostrophe should never be used to form the plural of ordinary nouns, names, abbreviations, or numerical dates.

The Chicago Manual of Style says:

Capital letters used as words, numerals used as nouns, and abbreviations usually form the plural by adding s. To aid comprehension, lowercase letters form the plural with an apostrophe and an s.

The lowercase letter exception presumably exists because omitting the apostrophe can make the sentence much harder to understand (for example, "mind your p's and q's" is much clearer than "mind your ps and qs"). I don't know if the rule was different in earlier editions of Chicago, but it's very much in keeping with the guide's philosophy of prioritizing clarity and simplicity over prescriptivist rules.

It doesn't matter how many different authorities/style guides are cited - usage in this area has never been fixed, so it doesn't mean much to suggest the "rule has changed over time".

The use of apostrophes has always been less common, but it's been around at least a century (there, for example, the 1700's). It's also worth noting that (particularly in earlier years) writers would sometimes simply leave a space (i.e. - write the 1700 s).

Per other answers, I suggest only using the apostrophe in contexts where not doing so would make things hard to read (as in dotting the i's and crossing the t's). That's in line with my understanding that the general trend over many decades has been a reduction in the use of all punctuation where the primary justification was to follow "rules of grammar". Increasingly, the primary (or only) justification for punctuation marks is improved legibility.