Is it is fair to trust someone blindly because of his family bakground ??

The answer to this would entirely depend upon one's own perspective and opinion. However, here is a sample idea for your reference:

Up to an extent, characteristics are supposed to be inherited and thus, passed on from one generation to another. However, one can't blindly trust without any rational thinking. One needs to stay cautioned because family background is part of the other million things that shape a person's character. To begin with of course a fine background creates a good impression but that is not enough. Experiences and people add on to one's thoughts actions and personality as well.

Happy to help!