When, why, and how did cordwaining and cobbling become distinct trades? All I can find is that there were laws barring cobblers from using new leather in England in the 11th(?)-14th centuries and that there's uncertainty as to the etymology of "cobbler." Thanks!

I don't have a proper ref to hand, but in London at least The Cordwainers' Company existed since late C13th.

But here's a terminus ante quem, some poor bastard of a cobbler makes a pair of shoes, and the wardens of the shoemakers (presumably the cordwainers) take them away from him:

Rauf John, of the citee of London, cobeler..for the sustentacon of hym, his poure wif & children made certain peyre of shoes, for the whiche makyng the wardeyns of the shomakers toke from hym the said shoes.

(1473-4 Proc.Chanc.in Cal.PCEliz. 1.p.xciv)

...

And it's not that simple either: for example there is a sumptuary law in England about excessive shoe length that includes cobblers as making shoes:

That noo persone Cordewaner or Cobeler..make or doo to be made..eny Shoes, Galoges or Botes, with eny other pyke that shall passe the lengh or mesure of 11 ynches.

(1464 RParl. 5.566b)

unless the cobblers were just pimping the shoes, not making new ones...