I doubt that it's possible to create a system that has NO intrinsic feel or baggage to it. But it's a fact that some systems have a lot more than others.
True20 seems quite adaptable to me. It's a natural for the Star Wars Force, for example, which one can't say of the D&D magic system.
Basically, True20 slants toward "psychic" type powers. You don't tend to have massive combat magic like in D&D. (Which to me is a plus.) There are a few holes in the system for some desirable settings, but they're pretty easy to plug. (Steve Kenson's "Psychic's Handbook" is invaluable in this regard. I hope some of those powers make it into the True20 hardback.)
Magic in Middle Earth tends to be so subtle and behind the scenes that I'd think it'd work fine with True20. (I'm not sure what ruleset you're referring to, though.) I'm not very familiar with the Harry Potter universe... though from what I know, it should work. You might want to be a bit more forgiving about people using Conviction to gain temporary powers they haven't formally bought.
"All right, I am not the Shadow. You have nothing at all to worry about. Except, oh, wait, I'm pointing a gun at you."