That' s a good question Flange Bracket.
A quick look at the IAA website tells you that Aircraft Registration is covered by SI 634 of 2005. Section 9, Sub Sections 3(a), (4) and (5) seem to be most relevant.
3(a) says that the owners name and address must be on the register.
(4) says anyone can inspect the register for a fee at a place and time decided by the IAA.
(5) Says anyone can have a copy of a register entry again for a fee.
Presumably a lot of this was drawn up at a time when the register consisted of a big ledger and the Internet was unheard of (even though it's an order from 2005!).
Therefore the IAA don't need your permission to broadcast your name & address, because it's the law!
The general public do not have access to the National Vehicle Register - you can't just look up someone's car registration number on the internet or anywhere else - only the Gardai and other state bodies like Motor Tax offices etc can do that. So why should aircraft be any different?
The register sometimes gets used as a source of marketing information but in fairness I have only had 2 instances of that in just over 4 years of having my name on the register.
The biggest problem about it I would say is that many people might make the mistake of thinking that because someone has an aircraft registered in their name, that that means they are "High Net Worth" individuals, whereas the reality for most GA people is that they are not wealthy but put everything into aviation. The general public doesn't know the difference between a tax exile's Learjet and a microlight!