What things can conservatism NOT do without, when boiled down to its core?

To be fair, those points (minus the free child care) are the official position of the Roman Catholic Church. American archbishops have been known to collectively push for immigration reform, for instance. The official church has been hard to place in a left-right political dichotomy, the obvious conservatism of male-priests-only notwithstanding.

Unfortunately, many American Catholics cafeteria into the anti-abortion (and anti-birth-control) position without the fair wages, pro-immigrant, or anti-death-penalty positions. (Many others cafeteria out of anti-abortion and anti-birth-control, and are usually the ones derided as cafeteria Catholics, but the “cafeteria” label should go both ways.)