The ACT Libs were one of the first Branches to be taken over by the "big C" religious Conservatives. They essentially threw out a popular moderate sitting Senator in Gary Humphries and installed the Abbot-backed Zed Seselja. They haven't been able to take a majority in the Territory Assembly since 2001. In the 2022 Federal election the ACT Liberals took zero out of three HoR seats and zero Senate seats (where Seselja was beaten to the second seat by independent David Pocock).
The ACT is an interesting case study in how the Liberal Branch can move in the opposite political direction to the electorate as a whole and maintain that loosing stance over several electoral cycles - to the point that they now trail both Labor and The Greens in the overall vote and can loose to centrist independents when they field right-wing candidates. After twenty years, Labor and The Greens have established an effective working partnership at the Territory Government level and, despite some issues in several areas of the administration, are unlikely to be seriously challenged at next year's Assembly election.
