If conservatives believe in individual liberty, it seems strange that they would support government intervention in something so intimate and personal as abortion.

You don't have to be a conservative or religious to be against abortion. Abortion being "intimate" and "personal' is entirely irrelevant because in their eyes it is murder. They are for protection of people's civil rights and protection from being murdered is a civil right. If you concede that a fetus is indeed a human life you cannot kill it for your convenience. There is no getting around that. If you do not concede that a fetus is a human life then abortion is fine in your eyes.

Conservatives are not against the concept of family planning, they are against the government paying for stuff that people can pay on there own. They see people as individuals with personal agency who are responsible for their own actions. They complain about crime because people should not be committing the amount of crimes that are committed, government assistance because they should not have to work so another person can be unemployed. They see it this way- No one is forcing the woman to not use contraceptives and have a child out of wedlock, no one is forcing that father to leave, no one is forcing people to commit crimes. So they should deal with the consequences of their own actions by themselves.