the word Sidhe, means "faery mounds"...if you were to say "Aes Sidhe", you would then be saying "[people] of the sidhe"
People of the Sidhe originally referred to Tuatha de, but after several more invasions across the celtic lands, the tuatha began to be called "fae" as they were of the faery mounds.
When Christianity was finally spread, tuatha de were described as Faeries, or souls trapped within purgetory. This is where the idea that faerys and the like were found in "betweens" such as halloween, midnight and doorways came from.
Christianity became so large in Ireland because for once, Christianity had allowed itself to be molded into the society; especially in Ireland. The Tuatha de were mischevious fairy souls, no longer worth worship. Crosses were adorned in celtic art and many of the legends that made up Irish history were either distorted into fairy tales or made into something that was digestible to the Christian culture. Some gods, such as Brigid, were made into saints.
I know that there will be people that have a problem with what I just wrote, but that's just what I believe after hearing all these folk and fairy tales told to me by my grandfather and after being practically obsessed with Ireland.

At one point, I wanted to move to Ireland so that I could join the IRA (or rather, Sinn Fein...their political branch) so that I could help free Ulster...buuut after more research and after visiting Ulster, I have found that it isn't exactly....."Irish"....anymore...for lack of a better explaination...
I guess what I'm saying, is please don't be offended; it's just my opinion, and I'm sorry sorry sorry if I offend anyone!! *bows a million times*
Airelinn