Except the separation of church and state doctrine isn't found in the first amendment, just as Dr. Paul says. The first amendment states, in regards to religion:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof...
Meaning that they may not establish a national religion, may not give preferential treatment to any religion, and may not ban the practice of any religion. If the doctrine of separation of church and state were true we wouldn't have people sworn in on bibles, like say every President in the history of this nation.
His quotes about churches being more influential than the state are clearly taken out of context, as he's not saying churches should have more power than the government. He's saying that the government should not legislate morality, as it is the job of the individuals and their preferred religions to decide morality. He's also saying that private charitable institutions, such as churches, are a better way of giving than having the government force us to be charitable.
As for Ron Paul being "much like his Republican counterparts," let's get serious. Capitalism over corporatism, peace over militarism, and individual liberty over big brother are not hallmarks of the Republican Party.