Legally they were exempt because The Military Service Act (1916) applied to men "ordinarily resident in Great Britain" not men "ordinarily resident in the United Kingdom"
But practically, it would have taken more men to supress the inevitable uprising than they would have recruited. John Dillon MP said:
If you had passed a Military Service Bill for Ireland, it would have taken 150,000 men and three months' hard fighting to have dealt with it.
The Easter Risings made it clear things were very unstable in Ireland, and they didn't want to make things worse. The backlash that followed their later attempt to apply conscription to Ireland (The Conscription Crisis of 1918) shows their first decision was correct.
This exchange in the House of Commons in 1918 between the Prime Minister and two Irish MPs shows the mood of the time:
§ The PRIME MINISTER [...]Therefore, we propose to extend the
Military Service Act to Ireland under the same conditions as in Great
Britain. As there is no machinery in existence, and no register has
yet been completed in Ireland, it may take some weeks before actual
§ Mr. FLAVIN It will never begin. Ireland will not have it at any
§ The PRIME MINISTER But there must be no delay.
§ Mr. FLAVIN You come across, and try to take them.
§ The PRIME MINISTER As soon as arrangements are complete, the Government will,
by Order in Council, put the: Act into immediate operation —
§ Mr. WILLIAM O'BRIEN That is a declaration of war against Ireland