Joseph, Bogen
No one is refuting that the ger is born anew and has no biological relationship to his parents. But that’s very different than saying “there can be no socializing with them, that’s the halacha.”
True, a convert has the same relationship with his previous parents as with his next-door non-jewish neighbor, but he can certainly be on great terms with his neighbor! the big one: “a jew cannot socialize with a goy”? That statement was bound to be taken out of context. A Jew is not supposed to get into a personal relationship with a goy, and in general we are meant to keep ourselves separate from the goyim. But in the case of a convert, each ger should take counsel from their own Moreh Derech in how to treat the people that brought him into the world. If they supported their child in his quest for truth (which sometimes happens) and the minute the child toivels in the mikveh, he cut these kind gentiles out of his life, that can cause a major chillul Hashem, which is also Assur.
I know of a giyoress who had very supportive parents throughout her journey into yiddishkeit. At her chasunah, (she married a BT) her (ex)father not only paid for the wedding, but spoke and said that he considers it a supreme honor that a child of his joined the chosen peeople.
The couple still visits them and such, though it can be challenging to raise children in a family where “Grandpa” is a goy.
In many cases the family disowns the child for converting (or they think he went crazy and and the conflict erodes the relationship) When that happens, it may be easier in a way because then there are no goyish “relatives” to deal with. Otherwise, I agree with cherrybim completely.