There are "real" sessions in Dublin but I've not found any in the city centre tourists spots. It depends what you'e looking for.

I've been to the session in The Lighthouse at Howth a number of times and despite being a banjo playing Scot was made welcome.I have heard it's now closed - going to be turned into flats - hope I'm wrong. Also found good friendly sessions in Dingle.
There's obviously a place for the "paid performer" session in the likes of Temple Bar but in these sessions there is not ( or does not appear to be )the same willingingness to let the visitor join in.