pick pockets?

In a broad daylight on Grafton St. in Dublin I personally saw someone get mugged.... Ireland has issues with junkies.
Keep in mind the other purpose of money belts, they protect you from simply loosing/misplacing your cash/cards/passport. IMO that's a greater risk than pickpockets. But either way the consequences are the same: If they go missing you'll have to waste a couple days out of your vacation to replace those items. For peace of mind use a money belt type device or the hotel-room safe.

I use a money belt in New York city. Just about anytime we are traveling. Even if the probability is only 1%, I just don't want to be inconvenienced. After years of travel, the money belt is second nature just like my socks.

I can't speak for men with wallets, but as a girl who lived in Ireland for a couple of years recently, it is a very safe place and I always felt completely comfortable carrying my purse. I usually just carry zip purse when I travel as well as it is something I am comfortable with and is part of my everyday life.

It isn't necessary to carry your passport with you at all times (especially in Ireland), so I would leave passport and extra money in a room safe.

Have a great time!

From Rick's Dublin chapter:

Pickpockets: Irish destinations, especially Dublin, are not immune to this scourge. Wear a money belt or risk spending a couple of days of your cherished vacation in bureaucratic purgatory--on the phone canceling credit cards and at the embassy waiting for a replacement passport. Wasting vacation time this way is like paying to wait in line at the DMV.

Dublin/Galway was the only cities I felt I had to be aware of my surroundings and my wallet.

Dublin has a issue with homeless people like any major city, so its best to stay with big crowds. I did however see plenty of Garda "Police" around on bikes or foot so I suppose if you have an issue they are close by.