I've never seen any statement of what political affiliation Randi claims, so I don't know why you are saying he's a republican.
The termination date of his challenges are public knowledge, so if nobody can claim it in the decades they are up, that sure as hell isn't his fault.
Of the various cases of people backing out of his challenge, Randi was never the one to back down.
As to things known about for centuries being true, I take you are including the sun going around the earth as it's attached to a giant crystal sphere, as well as the heart being the source of intelligence in humans, and that any illness can be cured with bleeding and prayer? Yeah.... Just because it's an old superstition or scam doesn't mean it works, even if it's clung around among the desperate and ignorant for centuries.
Besides, Homeopathy was invented in 1796 by Samuel Hahnemann. Yes, it's been around for centuries, barely, but it still hasn't been proven to work any more than telling someone you have magic pills that will cure them. Come to think of it, that's pretty much all homeopathy does.