In NSW public schools we have a list of values which we explicitly teach as well as the implicit teaching of values through rules, discussions etc. I do think that it the parent's job to be the main teacher of values.
There are some schools trialling Ethics education for children who do not attend scripture/religious education in public schools.
same in WA and Vic,when I was teaching.
we might send DD to private school, but we don't want her receiving RE (and it underpins the local curriculum, so you can't opt out) so I'm considering homeschooling.
her values and ethics will be instilled at home.