In Matthew chapter 10, Jesus warns his disciples that following Him would mean persecution, but tells them that those who lose their life for His sake will find it. Our focus, as believers, is not to pursue liberty in the realm of politics, but in the spiritual realm. Believers will come up against a conflict between political liberty and Truth eventually, since the Truth will get you persecuted. I am more afraid for those American Christians who are leaning too heavily on the importance of political liberty. True liberty is found in the spiritual realm, not the political realm. Nobody can take away your spiritual freedom! Your political liberty can easily be taken away, and human governments are not to be trusted that the liberty they offer is secure.
The statement, "True liberty will not cost others their liberty" refers to spiritual liberty, not political liberty. Political liberty always costs somebody. People die in war. This kind of liberty is a false reassurance of peace and justice. All you gain in war must constantly be defended by military might.
Although I enjoy living in a country of these relative freedoms, I don't focus my hope on it. My hope is in the One who offers eternal life.