I think political correctness has gone mad these days.
It really is (in my opinion) not WHAT you say, but HOW you say it.
If something is being said and it is meant in a derogatory tone, then yes, by all means take offence and object, but not everything is so simple.
I have plenty of irish friends, they will happily describe themselves as "paddys" and will say round about the 17th March.. "oh you have to come out, its paddys day".. etc..
As for the saying of a child "having a paddy".. anyone taking offence at that is really just looking for an insult where none is meant. It may possibly have had irish connotations a couple of centuries ago, but is certainly not a racist insult nowadays, and is just a phrase to describe a child having a tantrum, nothing more, nothing less.
I have worked in construction (albeit on the admin side) for most of my working life, and nicknames pertaining to a persons hair colour, build, race, nationality etc are commonplace, and are meant in a jocular way, with no malice whatsoever.
I agree that if someone feels insulted then they should speak up and explain their grievance, and the person using the phrase should respect that, and refrain from using it, but talk of compensation, tribunals and the way people these days get so upset over something that is most likely not meant to be nasty is a tad silly.