Here's WPUK's piece on the Irish law:
womansplaceuk.org/the-irish-question/
However, the Act also allows people to be treated differently on the basis of their ‘gender’ in all of the following circumstances:
People can be treated differently in relation to cosmetic services that involve physical contact – for instance, hairdressing, body waxing, and so on;
People can also be treated differently if there is a risk that you could be embarrassed because of a lack of privacy;
People can be treated differently at sporting events if the differences are reasonably necessary and relevant and, in relation to educational establishments, having regard to the nature of the facilities or events.
Insurance companies may differently decide how much to charge people for annuities, pensions, insurance policies and so on, based on different risk assessments, if the differences are based on proper research and statistics (although EU law proscribes the limit of this exemption in so far as men and women must be treated the same).
People can be treated differently if it’s necessary for a drama or entertainment production.
A person making a will or a gift is entitled to choose whoever they want to benefit.
Services may promote or favour the special interests of one person or group over another.
Goods and services which can be reasonably considered as being suitable only for the special needs of certain people may be provided.
In shared accommodation people may be treated differently in relation to personal privacy where lack of privacy might cause embarrassment.
When the accommodation is provided by a person in their private home, if for example a home-owner took in a lodger.
When housing is provided by or on behalf of the Minister for Justice and Equality.
When the accommodation is reserved for a particular category of people.
Single sex schools are allowed.
Institutions providing religious training to ministers of a particular religion may admit students of only one ‘gender’.
Third-level or adult education institutions may treat students differently by way of traditional university sponsorships, scholarships, bursaries, and so on.
Clubs may be established for a particular group of people.
Any person can be refused goods, services or accommodation if an experienced provider believes that there would be a substantial risk of criminal behaviour or disorderly conduct by that person, including abusing the service and causing trouble by being abusive or aggressive.
A person may be treated differently because of a doctor’s clinical judgement in relation to the person’s medical condition.
Funny how UK TRAs never mention all these exemptions, isn't it?