This is the reverse of this question, in a sense.
Suppose that a Gentile intermarries and he has a son who is Jewish. Later, the Gentile converts. Is the biological son ever halachically obligated to honor his father?
There are, possibly, two factors:
1) There was no "halachically" valid marriage. So the "confusing mix", here, is that while the son was born to a Jewish mother making him Jewish, because this was an intermarrriage, there was no Jewish marriage and thus, perhaps the biological father is not halachically his father.
2) After conversion, the father becomes like a newborn and severs all previous family ties. Thus, his biological son is not halachically his son, anyway, now.