I care about schools. I want them to be free and public.
I care about crime. I want to abolish the police and use that money to on social safety net programs including healthcare, social workers, housing, and more which is proven to reduce crime.
I care about children. I want paid parental leave for both parents, guaranteed job return, free childcare, free healthcare for children, and a monthly check for groceries.
Conservatives want none of that, and actively work against every point. Centre/centre-left only want some of that performatively and will undermine any implementation of these programs. The only people working for this are the “hard left.” And because of decades of anti-communist propaganda, no one will touch it.
The only reason I can think of to be conservative and “socially liberal” is to protect your own capital at the expense of others while not wanting to feel bad about doing it.