Key issue here is this is a male parent acting on behalf of a child to get the child Irish citizenship
AND
He is acting on his own behalf to pass on citizenship by being recognised as woman.
So this will be down to the law on birth certs and citizenship application requirements.
ARTICLE 9
1 1° On the coming into operation of this Constitution any person who was a citizen of Saorstát Éireann immediately before the coming into operation of this Constitution shall become and be a citizen of Ireland.
1 2° The future acquisition and loss of Irish nationality and citizenship shall be determined in accordance with law.
1 3° No person may be excluded from Irish nationality and citizenship by reason of the sex of such person.
2 1° Notwithstanding any other provision of this Constitution, a person born in the island of Ireland, which includes its islands and seas, who does not have, at the time of the birth of that person, at least one parent who is an Irish citizen or entitled to be an Irish citizen is not entitled to Irish citizenship or nationality, unless provided for by law.
2 2° This section shall not apply to persons born before the date of the enactment of this section.
3 Fidelity to the nation and loyalty to the State are fundamental political duties of all citizens.
Catch 22
There is likely /may be a clash of rights which should result in the State step in and act on behalf of a citizen child.......
But even if the High Court judge accepts the father acting on behald of the child the HC must take account of the Childs Constitutional rights as if the child is a citizen
The father:
He is male under Irish GR legistation. So his UK GRC means nothing as they are not "recognised" and the Minister can refuse to issue an Irish GRC
https://www.irishstatutebook.ie/eli/2015/act/25/section/11/enacted/en/html#sec11
Requirements on application where recognition in another jurisdiction
11. (1) A person who has changed gender under the law of a country or territory, other than the State, may apply to the Minister for a gender recognition certificate.
If he has no GRC his childs birth certs is not covered by the GRA2015
Uk legal case should have resulted in him being registered as the father on the childs birth cert.
Woman and Mother have specific meaning under the Irish Consitution and the word sex is used in the citizenship section.
https://www.irishstatutebook.ie/eli/cons/en/html#article41
THE FAMILY
ARTICLE 41
1 1° The State recognises the Family as the natural primary and fundamental unit group of Society, and as a moral institution possessing inalienable and imprescriptible rights, antecedent and superior to all positive law.
1 2° The State, therefore, guarantees to protect the Family in its constitution and authority, as the necessary basis of social order and as indispensable to the welfare of the Nation and the State.
2 1° In particular, the State recognises that by her life within the home, woman gives to the State a support without which the common good cannot be achieved.
2 2° The State shall, therefore, endeavour to ensure that mothers shall not be obliged by economic necessity to engage in labour to the neglect of their duties in the home.
https://www.irishstatutebook.ie/eli/cons/en/html#article42
CHILDREN
ARTICLE 42A
1 The State recognises and affirms the natural and imprescriptible rights of all children and shall, as far as practicable, by its laws protect and vindicate those rights.
2 1° In exceptional cases, where the parents, regardless of their marital status, fail in their duty towards their children to such extent that the safety or welfare of any of their children is likely to be prejudicially affected, the State as guardian of the common good shall, by proportionate means as provided by law, endeavour to supply the place of the parents, but always with due regard for the natural and imprescriptible rights of the child.
2° Provision shall be made by law for the adoption of any child where the parents have failed for such a period of time as may be prescribed by law in their duty towards the child and where the best interests of the child so require.
3 Provision shall be made by law for the voluntary placement for adoption and the adoption of any child.
4 1° Provision shall be made by law that in the resolution of all proceedings—
i brought by the State, as guardian of the common good, for the purpose of preventing the safety and welfare of any child from being prejudicially affected, or
ii concerning the adoption, guardianship or custody of, or access to, any child,
the best interests of the child shall be the paramount consideration.
4 2° Provision shall be made by law for securing, as far as practicable, that in all proceedings referred to in subsection 1° of this section in respect of any child who is capable of forming his or her own views, the views of the child shall be ascertained and given due weight having regard to the age and maturity of the child.
This will have implications for children who have independant rights from their parents.
If the citizen father can obtain citizenship for the child under the current system he is not acting in the best interest of the child by rejecting the process he can follow to have the childs citizenship recognised.