Please note that words used have sensitive political meanings.
'Ireland' can (in different contexts and with differing background and intent of the person using it mean either
- an Island
- the Republic which covers part of said Island.
For many people, what you said does not make sense. Ireland has no borders with anything else -- it is surrounded by sea. Personally I cannot think of any Irish or British person (whether Nationalist. Unionist or Indifferent) background that would ever write something that implied Ireland stops at the border with the Province.
I know what you MEANT, of course. I would have written
'There are no immigration controls between the Republic and the United Kingdom.' which is neutral, uncontroversial and objective.
(There used to be pretty often security controls all over the border area on the N. Irish side, with an army person carrying a machine gun but they, thankfully, have almost disappeared).
Actually there are regular controls, but in one place only. The Gardai have checks on persons for ALL arriving flights into Dublin -- but if you are British or Irish, and you are travelling from the UK, under the Common Travel Area agreement you don't need a passport to go through.
(These days the Gard on duty will ask for a form of ID like a driving licence, which he or she know you must have to check in with the airline at your departure airport)