Well, I am 19, so I may not be the general "Christian Conservative" but I do have a good perspective since i've been to church my whole life and want to double major in Religious Studies and Economics.
In my experience, the easiest way to explain the freedom and liberty mindset to an evangelical is like this. God gave and continues to give humans freedom of choice. ie sin, lust, foul language, sin in general. He didn't force us to live the right way, which makes our choice to live that way all the more special. We (Ron Paul Republicans) want every person to be allowed to do and say as they please. You be able to follow your religion and what it says, and a gay person to do what they feel is right for them. Since you have free speech you can talk to them, and tell them that you think they are wrong, but the ultimate decision is up to them. This is what God did for us.
Then they usually say that if we let everyone do what they want then abortion will be allowed. At this point you bust em with something along the lines of 'This freedom is allowed as long as no one else's rights are infringed upon. And in the case of abortion, the right of the baby is infringed upon, its right to life.
Sorry for the long post, but I have found this works pretty well...