As it happens, some research I was recently doing on behalf of another denizen of /r/AskHistorians/ ties right into this. Eoin Mac Neill, a founder of the Gaelic League in Ireland, learned Irish from the Aran Islanders in the 1890s, and received letters from them into the early 20th century. He also wrote a few letters home to his brother during the summers he spent there, describing life in the islands.

First and foremost, they were very isolated. They knew of their own way of life, and they knew the 'mainland' was there. But they visited it only long enough to sell their catches of fish, and collect post and people travelling to the islands (and maybe some extra milk). The only outsiders living long-term on the islands were the occasional priest and the even more occasional school-teacher, although there don't seem to have been many of the latter during Mac Neill's stints there.

An illustration of the isolation is that Mac Neill asked his brother to send him a packet of 'American Wonder' peas, because the islanders didn't know what they were, and he wanted to give his host family some to plant. They 'haven't a ghost of a notion' what peas were, he wrote. The main diet was potatoes, fish, seabirds, and milk, with very occasional meat and a small amount of bread. Farming was a bare subsistence, and nearly all the men on the islands farmed, fished, and hunted as necessary.

They spoke Irish, with a distinct dialect, among themselves, and many of them only spoke 'a little' English (although the English in the letters they wrote is perfect, if a bit archaic even for the 1900s). Oral traditions were still very strong, and the strain of Catholicism that persisted among the islanders owed more to the pre-1800s late-'Celtic Christianity' than more conventional Roman Catholicism. This was fading under the influence of some particularly authoritarian priests, but was still there. Alcohol consumption wasn't nearly as common there as in the rest of Ireland, mostly owing to plain unavailability.

There was no electricity on the islands until the mid-20th century (though admittedly there were houses elsewhere in rural Ireland that only got electricity within my memory; I was born in 1977), and the only way to them was on small boats. In the rough conditions of Galway Bay, particularly in winter, the islands could be cut off for weeks at a stretch. In these conditions, it wasn't possible to fish, either, so there were stocks of dried fish put by. Mac Neill wrote approvingly of these, saying that some of the dried ling was 'like a board',a nd wanted his brother to buy some from the islanders. There was no doctor, no particularly regular postal service, few enough of even horse-drawn vehicles, certainly no cars, and only maybe the odd bicycle by the early 20th century.

The letters written by the islanders come across very strangely. Many of them say that they are 'lonely' since Mac Neill left, having nobody but the few dozen people they'd known all their lives to talk to. Sometimes they're looking for work, or a letter of recommendation, but mostly they'd like him to come back to the islands. They acknowledge gifts and money he'd sent, but seem a little bemused by them - possibly some of them they didn't know what to do with, although that's not entirely clear.

Apart from a higher level of literacy, and some better tools and the bicycles, it seems like you'd have been hard put to distinguish life on the islands in the early 20th Century from life there in the late 18th Century.

Source:

The Mac Neill Papers, National Library of Ireland.