There is a luxury department store near my office that opens its Christmas dept in late August (it was late July a few years back). That is up on the top floor, and while it's a reasonable size and reasonably prominent THERE, you DO have to go all the way up to find it. And there is no other bit of Christmas around the store yet and won't be until at least end October, more likely November.
This store is famous for its window displays at Christmas - and they won't be in place until late November.
So while it is there for those who want it, it really isn't "in your face", and the only Christmas music there is if someone has set off a musical box or snowglobe.
I admit, I went in last week to explore the decorations - because they are always gorgeous and the nice ones are always sold out before October. I am pondering getting a couple of new ones (lovely peacock colours), but I will wait until next week before deciding properly.
Other than that, on the main (posh) shopping street in the capital city, there are no other signs of Christmas yet. There are a few decorations in the luxury goods shops - Waterford Crystal and Belleek China types - but they are there all year round as part of the general offerings to US and Asian tourists in particular. And they are part of the normal display of all sorts of goods from those types of brands, not a specific Christmas display.
The outdoor shops are selling off tents and getting in hiking and skiing gear.
The fashion stores are starting to have jumpers and trousers, and lovely stripey wrap dresses.
The chemists are still displaying sun lotion and hay fever remedies, although "care of the feet" displays are getting more prominent. And I did hear one pharmacy assistant talking about the "winter skin care promotion" starting in 2 weeks time.
The card shops are still full of birthday, weddings, new baby, and exam congratulations cards, with a display of "good luck in school/university" where the Communion/confirmation ones were in late spring. No Christmas cards available yet.
Jewellers still have normal displays, with fake flowers amongst the diamonds rather than holly.
Tiger still has jolly fruit and Pride themes going on.
So if you are looking to avoid Christmas, apart from 1 department on the 3rd floor in the luxury Department store, please come to Dublin and enjoy!!