Vitiligo on fingers. Blank on this part.

My father (age 68) has white spot near his fingers and no where else in the body and I don't have any spot in my body and my age is 29, I was about to marry a girl but the girl's family rejected the proposal by having a great confusion in their mind that the problem my father has can be spread to the next generation of mine. I explained them many times this isn't the case but they are in confusion and they told me this thing happen in their nearby society. I don't know much about it whether this is any hereditary disease and how bad it can impact my next generation as I don't have any mark of this on me. If there assumption is correct then its fine for me but if they are wrong how can I convince them , I am totally blank on this part.