Australia’s constitution was partially based on that of the US. We are also a federation of states, with a federal Senate in which the least populous state has the same number of senators as the most populous. So we have rather similar potential for “blocking minorities” as the US.

And yet we have a reasonably liberal abortion regime nationwide - which is not due to the courts (we have no constitutional right to abortion), but simply the outcome of the democratic legislative process in each state. I think it never became quite the political/cultural hot potato here as it did in the US, in part because it was left up to elected officials rather than unelected judges. Even if someone doesn’t like the current situation, it is harder to object to the legitimacy of it when the people the voters voted for are responsible for it.

I think one relevant difference is that as a country with a smaller population and a shorter (post-colonisation) history, there is arguably less inter-state cultural diversity in Australia. We don’t really have “red states” and “blue states” - some states lean more one way than the other, but it is much less polarised than the US.