I've got some 1/4 inch Manila rope that's really, really curly. It ends up very tangled and difficult to manage. Is there a way to straighten or relax it?
Yes there is. Soak the rope, then hang one end of the rope from a high point, and put a plumb bob on the other end. A plumb bob is just a fancy weight, you can use anything with some weight to pull the rope straight.
Let the rope hang until it's dry. It will be mostly straight at that point, but it will never be perfect.