The word Conservative requires no modifying adjective because it means both fiscally and socially conservative. What you describe here, as I pointed out before, is a liberaltarian.
The left hijacks enough terms of art as it is, as I see it there's no need for the liberaltarians to do the same.
But what do you call a person who is a strong opponent of abortion, same-sex marriage and strongly supports such things as prayer in schools and the posting of the 10 Commandents . . . . however, does not mind the federal government spending like crazy and running up the debt and thinks that open borders aren't a bad idea?