Jumping in a bit late here, but we're considering this name for our first child, and I wanted to offer my perspective.
I'm an American with Irish heritage, and I did not first hear of the name from Saoirse Ronan. I discovered her after scouring baby-name boards and coming across the name Saoirse. I love the sound, and I adore the meaning. I agree that anyone who uses this name should do it with their eyes wide open, because it does indeed have ties with not just a freedom movement, but one that has committed violence in support of its cause. However, it need not be limited to that meaning. I like the name simply because it means "freedom," I'm a great lover of freedom and liberty, and I'd like to bestow that ideal on my child.
On the downside (and the reason we haven't committed to it yet), we're worried that the child will grow weary of having to spell and pronounce her name for everybody. I once worked with a Siobhan, and no one in our workplace ever seemed to have trouble with her name, although I'm sure she must have had her share of struggles through the years.
As for pronunciation, it's true that there's an "er"-type syllable in there that gets rather glossed over, so that if you were speaking it slowly, it would be something See-ur-sha. But in normal speech, the first two parts get blended together into Seer-sha.
I believe Seer-sha, Sir-sha, and Sair-sha are all legitimate pronunciations. Much of it simply depends on where you live -- just as a person from Boston might pronounce things differently from a person in Atlanta.