Pluralize the noun-as-adjective

I've never been sure about this.   In the computer world we have "systems programming" and "applications programming"; it seems to me the terms would be exactly as clear without the plural form, but unlike you I was never formally taught that the plural was wrong so on the rare occasions when I stare at them, trying to figure out whether it makes any difference, I always end up shrugging and moving on.

Are there any examples where it makes a difference?   Is there any phrase where horses breeding means something different from horse breeding (plug in your own nouns here)?   Maybe that would shed some light on this question.

This has been one of my pet peeves ever since Martha Stewart Living magazine started saying "See the Recipes section."   The Chicago Manual of Style (sections 5.22, 7.25) calls these attributive nouns. If the singular can cover the plural, it works: tax attorney. If the meaning could be ambiguous, maybe use the plural: antiques store (not an antique, old, store) (?). Chicago also adds the apostrophe if the possessive is meant: workers' party. (Often the apostrophe gets dropped because it's a pain to know where to put it -- Worker's Party or Workers' Party?).   If this has been discussed on the show, which episode was it?

I don't recall it on the show, but it was discussed somewhat at this forum at this link:

https://waywordradio.org/discussion/topics/baby-singular/?value=baby&type=1&include=1&search=1

Bob Bridges said:

...Is there any phrase where horses breeding means something different from horse breeding (plug in your own nouns here)?   Maybe that would shed some light on this question.

This is a farm boy's take on the above that are different to me. My dad's first cousin did horse breeding on his farm. The act of copulation between a stallion and a mare could be called horses breeding.

Emmett