It absolutely does mean freedom from religion. There are many of us who do not believe God exists and people who believe in things other than the Bible. Freedom of Religion exists only where the Government is religion neutral. We the people have the right to practice or religion and to have freedom of religion only in an environment where the government is religion neutral. I do not have the freedom to believe in reality if Christians and Jews don't have the freedom to believe in the invisible guy in the sky.
Christians seem to like the idea because they think it's free money.
Freedom of Religion also means Freedom from Religion for those who do not want to participate in Religion. What they don't realize is that government money equals government controls and that Uncle Sam isn't going to just write a check for 250 billion dollars and tell churches to spend it in whatever manner the Holy Spirit leads you. Government money comes with all kinds of government requirements on how to spend that money and will turn churches into agents of the government. What will happen is that people will stop giving their money to the churches because they expect the Government to do that for them. Lieberman's Lack of Faith in God Joe Lieberman started his campaign talking about his religion and his faith.