I actually don't really know what they mean by freedom. This might be my 'centrist' bias talking, but when I think of republicans that I've had around me in my life, I roughly estimate that they think freedom is hierarchical. And the sort of freedom that you get, is roughly a combination of positive and negative freedom (in the technical sense). That is to is say, it seems to me to be more like 'power' than freedom - which is to say, that the 'is-ought' problem remains as freedom/power is gained. The 'left' also may have 'power' issues in my estimation
But I don't really know. I guess I don't understand the republican/democrat ideas about freedom/power, and instead work on defining those things myself. I think it is important to solve the is/ought problem, as freedom and power is exercised. That is to say, that think the exercise of freedom/power is legitimated by having goals/actions that are Just. Recognition of the corruptibility of freedom/power seems never to be discussed on either side as self-criticism.
I think you're hitting upon the great contradiction which has existed in this country since its founding nearly 250 years ago. To use George Carlin's description, "This country was founded by slave owners who wanted to be free."
As for power, at least the Founders were wise enough to realize that they didn't want power to rest solely with a single individual, faction, or state. They favored a separation of powers between state and federal governments, as well as a system of checks and balances between the three branches of government.
My observation has been that conservatives tend to focus on economic and business freedom. Religious conservatives also tend to support the same agenda, although obviously favored towards the predominant religion.
When it comes to abortion, I've always considered it a medical issue and my opinion is that it should be left in that realm. A matter between doctor and patient. The law need not get involved in that.
However, on a philosophical level, I can see where some might view a human fetus as a human life - or at least having the potential of being such. But as a philosophical question, I sometimes wonder how it came to be that it was automatically a liberal/conservative issue.
It seems to have turned out that way in practice, although there are those who are mostly liberal yet oppose abortion, as well as those who are mostly conservative yet favor abortion.