As I understand it, people on the right like the Republican party because they like the idea of less government, less taxes...(which is an okay concept to me).
"Less government" means less government interference in areas that the government has no business being in. However, it is the government's legitimate function to protect the rights of the innocent citizens that it represents. It is the government's legitimate function to prevent one person from directly harming another. Less government, does not mean that the government should not be involved in preventing the infringement of the basic rights, the right to life being the most basic of all.
But if they're against abortions because of some moral high ground, then they're in favor of more government to police everyone into accepting their morality, the exact opposite of what they want the Republican party to stand for.
Pro-life politics is basically not about the enforcement of morality, it is about the defense of human rights.