Keep in mind that the purpose of React is to better couple things that logically should be coupled. If you're designing a complicated "validate password" method, where should it be coupled?
Well you're going to need to use it every time the user needs to input a new password. This could be on the registration screen, a "forgot password" screen, an administrator "reset password for another user" screen, etc.
But in any of those cases, it's always going to be tied to some text input field. So that's where it should be coupled.
Make a very small React component that consists solely of an input field and the associated validation logic. Input that component within all of the forms that might want to have a password input.
It's essentially the same outcome as having a service/factory for the logic, but you're coupling it directly to the input. So you now never need to tell that function where to look for it's validation input, as it is permanently tied together.