Conservatism, as I understand it, stands up for core principals. For Christians for instance, that is Biblical Inerrancy and the Authority of God and His Word. Socialism/Progressivism seems to put man above God instituting human relitavism instead.
For instance in Social Justice stealing from the rich is justified by getting rid of "Thou Shalt not Steal". Abortion is justified by getting rid of "Thou Shalt not Kill". Homosexuality is justified by getting rid of "Thou Shalt Not Commit Adultery". It all comes down to getting rid of God and His word because it is inconvenient to men.
Liberals would tell you that Jesus advocated paying your taxes and helping the poor. They have just as much of a case as conservatives have. Christianity is simply not built on the same principles as American conservatism. There are elements of it that can be used by both sides, but it's a pick-and-choose business.