I have been wondering this also.This is the problem with Self ID really, who is going to enforce single sex provisions in the face of this?
Our Equality act also specifically states 'gender' instead of sex which is frustrating.
Basically it's a complete shitshow over here and the government don't seem to care.
According to this article from Womensplace UK -
Section 5 (2) (g) of the Equal Status Act 2000 provides an exemption that treatment of persons on the gender ground are permissible “where embarrassment or infringement of privacy can reasonably be expected to result from the presence of a person of another gender”. However the new coalition government proposes to “Amend the gender ground in equality legislation, to ensure that someone discriminated on the basis of their gender identity is able to avail of this legislation.” It would appear that the 78% male government elected in February plans to do away with the protection offered to women and girls, for example, who might want to retain single-sex toilets in school.
https://womansplaceuk.org/2020/07/13/gender-recognition-ireland/
The article is 2 years old, so I'm not sure if that has happened yet.
Here's another article which mentions exemptions -
https://www.irishlegal.com/articles/stephen-kirwan-pitfalls-and-uncertainties-in-ireland-s-gender-recognition-laws
Section 7(2) of the Equal Status Act 2000 specifically prohibits discrimination in relation to the admission or the terms or conditions of admission of a person as a student in an educational establishment. Further it prohibits the access of a student to any course, facility or benefit provided by that establishment. This general protection however is subject to two important exemptions.
The first exemption, contained in section 7(3)(a) of the Equal Status Act, notes that where an educational establishment is not a third-level institution and admits students of one gender only then section 7(2) is deemed not to apply. The second exemption, commonly referred to as the ‘ethos exemption’, is contained in section 7(3)(c) of the Equal Status Act. This exemption permits a school which, in pursuing the objective of promoting certain religious values, can legitimately refuse to provide the requisite accommodations for transgender students on the basis that transgender identity does not form part of the religious ethos of a school.
So it appears the religious schools are able to ignore it on the basis of their religious ethos.