IANAL, but I do not think there is any need to obtain exemptions.
The federal Sex Discrimination Act (linked in the other Australian themed thread) has as its clause 7D:
7D Special measures intended to achieve equality
(1) A person may take special measures for the purpose of achieving substantive equality between:
(a) men and women; or
(aa) people who have different sexual orientations; or
(ab) people who have different gender identities; or
(ac) people who are of intersex status and people who are not; or
(b) people who have different marital or relationship statuses; or
(c) women who are pregnant and people who are not pregnant; or
(d) women who are potentially pregnant and people who are not potentially pregnant; or
(e) women who are breastfeeding and people who are not breastfeeding; or
(f) people with family responsibilities and people without family responsibilities.
(2) A person does not discriminate against another person under section 5, 5A, 5B, 5C, 6, 7, 7AA or 7A by taking special measures authorised by subsection (1).
(3) A measure is to be treated as being taken for a purpose referred to in subsection (1) if it is taken:
(a) solely for that purpose; or
(b) for that purpose as well as other purposes, whether or not that purpose is the dominant or substantial one.
(4) This section does not authorise the taking, or further taking, of special measures for a purpose referred to in subsection (1) that is achieved
It would straightforward to establish that lesbians are disadvantaged and a measure to provide substantial equality would include events for the purpose of social support.
Even if that didn’t work, the organisations can use section 39
39 Voluntary bodies
Nothing in Division 1 or 2 renders it unlawful for a voluntary body to discriminate against a person, on the ground of the person’s sex, sexual orientation, gender identity, intersex status, marital or relationship status, pregnancy, breastfeeding or family responsibilities, in connection with:
(a) the admission of persons as members of the body; or
(b) the provision of benefits, facilities or services to members of the body.
so it is legal to have a voluntary body by lesbians, for lesbians. And a service could include an event. If a venue refused the booking, they would be the ones guilty of discrimination.
And federal law overrides state law so if anyone tried it on, the lesbian organisation would have resort to clause 11(3)
(3) This Act is not intended to exclude or limit the operation of a law of a State or Territory that furthers the objects of a relevant international instrument and is capable of operating concurrently with this Act.
So my take is that these organist don’t need an exemption, they should go ahead and let people try to shut them down, sue venues that cancel for discrimination on the grounds of sex and sexual orientation, and if the complainants try to use state law against then, use federal law and get the state law struck out. State law shouldn’t make illegal things that federal law explicitly allow.