I'll go the other way from
@Goro and
@gonnif .
Having a physician parent drastically improves one's chances of getting into medical school. Being in academics even more.
#1 When it comes to education, parents matter, a lot. Physician parent means growing up at least reasonably well to do. It mean ample resources and more often than not a home culture of education being important. Those are incredibly important when it comes to laying the foundation for a medical school application. I certainly have seen children of physicians go the other way, but compared to the average child they have an advantage.
#2 Fair or unfair, connections matter at every level of schooling and employment. I was asked at my Hopkins interview, "so I see that your father went to HMS, what will it take to convince you to come here over there?" People notice your parent's education levels and some care more than others. In my n=1 experience this tends to be a bigger deal in the Northeast.
#3 Lastly, connections are great, but at the end of the day the ability to leverage those connections are what is important. The vast majority of people don't understand this concept and thus you get the, "polite interview, polite waitlist, polite rejection". But, on average? Will help more than it will hurt.