The answer is that the Labour Party (specifically Peter Mandleson who was Secretary of State at the time, and George Howarth who was Junior Minister) made it so.
The House of Commons Disqualification Act provided that a person could be an MP and a member of a legislature in any other Commonwelth country. Why is another question. The Disqualifications Act 2000 added the Republic of Ireland to that provision. Why is an interesting question.
Here is the debate when the Bill was considered in Committee of the whole house.
As noted, it turns out that he will resign his seat in Parliament if he gets elected to the Dail, perhaps as a result of conflicting legislation in the Republic (but I don’t know).