Culchie etymology - many theories but I have never come across this one before.

Seems unlikely, because the word is documented in print from 1790, which is well before the establishment of boarding schools in Ireland to serve middle-class Catholics.

The most widely-accepted etymology is that the word is taken from the town of Kiltimagh, in the Mayo Gaeltacht. This suggestion is reinforced by the fact that the term "culchimach" appears in Behan's Confessions of an Irish Rebel as a mildly derogatory term for Irish-speaking people.

I always thought “Culchie” came from how Coillte Mach (Kiltimagh) was pronounced by locals to that area. In fact I have heard it pronounced as Culchie Maith.

Agreed, my husband's family was from Kiltimagh and he spent a lot of time there in the '50s. I have heard it pronounced with an 'i' sound, but mostly with a subtle 'ui' sound that would easily be interpreted by dubs as 'uh'.

If you regard it as a word originating in Dublin, it's very unlikely to have Irish-language roots; Dublin has really never been an Irish-speaking city; it went straight from Norse to English. Any Irish-speakers in the city were themselves recent arrivals from Gaeltacht areas; they were hardly likely to coin a degoratory term to describe themselves. Nor, it has to be said, during the period when Dublin was growing rapidly due to migration from the country - i.e. from the 1840s onwards — were people coming "from the woods"; the Irish forests had been cleared more than a century earlier. They were coming from farms.

If the word has Irish roots, the most likely explanation is that it originated outside Dublin, was brought to Dublin and then survived in Dublin when it fell out of use elsewhere.

But, it's still a fair question: Why Kiltimagh in particular? Well, remember that the Cromwellian settlement involved ethnically cleansing culturally Irish people from the rest of the country to Connacht? And, moreover, to rural areas of Connacht? It wasn't entire populations that were shifted; it was the class of for former landowers, leaders, chieftains, etc. The idea was that the demoralised, leaderless peasantry left behind would be more amenable to becoming good, loyal, Protestant, English-speaking tenants for their new Cromwellite landlords.

It was at best a partial success; conversion to Protestantism did not proceed at pace and it was centuries before the language was largely eradicated in the rest of the country. But it did leave parts of Connacht as a place where a more-or-less integrated Gaelic culture (integrated in the sense that it had a leadership class as well as a peasant class) survived — in relative poverty and opression, to be sure, but it did survive. And that established rural Connacht as a place that was, culturally, fairly alien to the most Anglo parts of the country, which were the larger towns. It's not impossible that a term like "Culchie" orginated in anglified or Anglo-established garrison towns in or near north Connacht and was only later transplanted to Dublin, where in time it was broadene to include not merely people who were distinctively Gaelic, but anyone from a modest rural background.

And there is the term 'living in the sticks' for someone living in a very rural area. Also the word used by English speakers to describe living in very rural bits of Africa, living in the 'bush'. Both used as slightly perjorative.

For many years Kiltimagh hosted the Culchie Come Home Festival which encouraged emigrants to return for a week's events.

The festival was discontinued due to falling attendance but revived in 2016 rebranded as the Coillte Come Home Festival.

https://kiltimagh.ie/event-listings/coillte-come-home-festival/