"We need more research" / "We don't know yet" is the homoepathic eqivalent of creationisms "Teach the controversy" ploy.
Homoepathy doesn't work. They've done studies on it. They haven't tested vague "things related to homeopathy" like "does water have a memory?", they have actually tested the 'drugs' themselves. They don't work.
It's not my mind that's closed, it's the book that's shut on homeopathy. It has been thoroughly tried and debunked as nonsense. What more is it, exactly, that you think an open mind should entertain vis-a-vis homeopathy?
Before you trot out the tired "flat world" defense, read Isaac Asimov's essay on degrees of wrongness. Our ideas have been getting better over time -- it's preposterous to propose that we could be as wrong about molecular biology, germ theory and medicine as we were about the earth's shape. We are wrong, but we know we are not that wrong.
Bitcoin is an actual thing that works (just 2 years after invention). Homeopathy has found no supporting evidence in 150+ years and it completely lacks even a reasonable mechanism. Apples and oranges.
And finally hiding nonsense behind "everyone believed the world was flat" is quite aggravating. Scholars have known the earth was spherical and even its approximate circumference for over 2000 years.