According to the Irish Government, who, of course, will probably defer to your exceptional expertise on constitutional law:
If you or your parent were born on the island of Ireland before 2005, you are an Irish citizen. You can apply for an Irish passport without making an application for citizenship...
Applications and questions about Irish citizenship are dealt with by the Irish Naturalisation and Immigration Service (INIS). We deal with Foreign Births Registration only.
www.dfa.ie
So let's make all those with convictions for Loyalist terrorism or support of illegal Loyalist organisations proper Irish and nothing else.
That website* doesn't reflect the intricacies of the legal position, contained in the legislation:
The electronic Irish Statute Book (eISB) comprises the Acts of the Oireachtas (Parliament), Statutory Instruments, Legislation Directory, Constitution and a limited number of pre-1922 Acts.
www.irishstatutebook.ie
In particular, see s.7 which differentiates people born in Northern Ireland.
You also need to consider Article 9(2)(1) of the Irish Constitution.
And s.6 of the Irish Nationality and Citizenship Act 2004.
This Wikipedia article explains the current position quite well.
en.m.wikipedia.org
In particular:
'The
Twenty-seventh Amendment was approved by referendum on 11 June 2004, and was enacted on 24 June. It inserted a new section in Article 9 of the constitution stating that, "notwithstanding any other provision of [the] Constitution", no-one would be automatically entitled to Irish citizenship unless they had at least one parent who was (or was entitled to be) an Irish citizen. The Irish Nationality and Citizenship Act 2004 amended
citizenship law to remove the entitlement to citizenship from those born on the island of Ireland who did not have an Irish-citizen parent, or whose parents had not lived in Ireland for three of the previous four years. This law was commenced on 1 January 2005.
[15]'
See here also:
en.m.wikipedia.org
In particular:
'Entitlement by birth, descent, or adoption
Edit
All persons born in the Republic of Ireland before 1 January 2005 automatically received citizenship at birth regardless of the nationalities of their parents.
[72] Individuals born anywhere on the
island of Ireland from that year on receive Irish citizenship at birth if they are not entitled to any other country's citizenship.
Otherwise, they are entitled to (but are not automatically granted) citizenship if at least one parent is an Irish citizen or holds an entitlement to Irish citizenship, a British citizen, a resident with no time limit of stay in either the Republic or Northern Ireland, or a resident who has been domiciled in Ireland for at least three of the preceding four years.
[73] Any person entitled to Irish citizenship who performs an act that only an Irish citizen has a right to do, such as applying for an Irish passport or registering to vote in national elections, automatically becomes a citizen.
[55]
Individuals born in Northern Ireland from 6 December 1922 to 1 December 1999 who did not have an Irish citizen parent were entitled to become Irish citizens by declaration. Any person born in that territory from 2 December 1999 to 31 December 2004 is
entitled to Irish citizenship regardless of the statuses of their parents;
[74] this includes children born in Ireland between these dates to foreign government officials with
diplomatic immunity, who are eligible to claim citizenship by special declaration.
[75]'
Essentially, anyone born in Northern Ireland before 2005 is
entitled to Irish citizenship (in addition to their British citizenship), but they're
not automatically citizens from birth. It requires a positive act. I'm unaware of any Loyalist terrorists that have taken that act to obtain Irish citizenship, such that it would be an option to the British government to strip them of British citizenship. Hence the fact that's not happened isn't an indicator of inconsistent use of the power (and that's before we come to all the other potential reasons for different treatment even if the powers could be used).
ETA: * that website demonstrably incorrectly conflates being a citizen with being entitled to to apply to become one.