I was rather shocked when I tried to get across from Copenhagen to Malmö with a Finnish national ID card, only to discover it wasn't valid valid for entering Sweden. Luckily they saw reason and let me through after a while but it must be horrible for the daily commuters.
When I lived in Copenhagen a few years back the commuters numbered in the 10000's. I can imagine that number has gone down a lot recently.
You were without a question dealing with an incompetent border officer in that case. Finnish ID card issued to a Finnish national is a valid travel document to all EU countries, to all Nordic countries, and to Switzerland. Additionally, for the citizens of all Nordic countries, no official travel documents are required to other Nordic countries in the first place. There is only a requirement to "be able to prove your identity on request" - for which a driver's license would usually suffice.
It is a bit more amusing than that, sort of a Catch 22 situation.
In neither Ireland nor the UK, nor for travel between them (except by 'plane) is one required to have or produce ID.
What one has to do (if asked, and then a right asserted) is establish one's right to enter the country. The easiest way to do that is via a Passport.
One can still travel (by boat) between the two countries w/o a passport, you just have to be prepared (if challenged) to argue and maybe waste some time.
Driving a vehicle in the the UK (and I assume in Ireland) is a situation where one can be required to produce ID (even then you do not have to carry it), but not in normal day to day life.
Does your regular ID state your citizenship? Good, then you can travel. If it doesn't, you aren't proving that you are a citizen with the right to travel freely in schengen.
I had a similar situation last November, when an over-eager Lufthansa check-in officer denied boarding the plane because I was using a Finnish national ID card. I was travelling from Finland to Croatia and the explanation was that Croatia had enabled passport checks on border and ID card is no passport.
No amount of explanation helped. I did have my passport with me and I showed it to this lady. Rest of the trip I used only the ID card.
Common theme seems to be, at least in Finland, that dealing with public agencies and authorities is just fine, but you can get to a trouble with private companies.
When I lived in Copenhagen a few years back the commuters numbered in the 10000's. I can imagine that number has gone down a lot recently.