No caravan site, club or commercial organisation is legally allowed to discriminate on grounds or race, religion, gender or ethnicity so there's nothing to stop members of the travelling community, Irish or otherwise, from renting caravan pitches.
If the warden went round with a flashing neon sign to show his whereabouts what would people complain about if the group of people that you mentioned have done nothing wrong?
Club officials may be uninterested because if they discriminate against any ethnic group they will be prosecuted.
That's the legal position, but in reality if there's something that you don't like about any site, simply vote with your tow hitch and go somewhere else.