It has been said that a convert must avoid aspects, or relics of their non-Jewish life, from before conversion. I have heard some rabbis say, all ties to genetic family are severed with conversion. The relationship with the old family must end. Is this true for all of Orthodoxy?
Unless there were extenuating circumstances at play, I think someone has gone too far here.
הגר אסור לקלל אביו הגוי, ולהכותו ולבזהו--כדי שלא יאמרו, באו מקדושה חמורה לקדושה קלה, שהרי זה מבזה אביו; ונוהג בו, מקצת כבוד.
The convert may not curse, strike, or demean his non-Jewish father; as people would say this guy has descended in holiness, as now he disgraces his father!; he should instead treat him with some amount of honor.
It's much easier to say none at all than have lots of difficult calls to make. Rabbi Berel Wein, for example, has said that a convert who keeps wanting to go to their non-Jewish family's Christmas party is bad news for everyone involved.
Here's an excerpt from the Rabbinical Council of America's conversion procedures; this is mainstream Centrist Orthodox (and a conversion they do will be recognized by the Israeli rabbinate). Emphasis added below.
Exposure to Communal Life by Living in an Orthodox community
As far as the halacha is concerned, conversion involves the creation of a transformed, fully reborn, new person. Becoming fully part of the Jewish family, one literally acquires a new family, a new life and as such one reorients one’s entire being. The candidate will be expected to cultivate new friendships, new relationships, new social activities, new Torah commitments. Moreover, as with any Jew, the growth and learning process continues throughout one’s life.
Requirements of Other People in a Candidate’s Life
When a candidate is previously intermarried or is converting for the sake of an individual Jew (as per above), the spouse’s observance level and attitudes must be consistent with the present and future Torah observance of the candidate and not be a source of conflict or opposition to the convert’s adopting a halachic lifestyle. The Beit Din should also consider whether other significant individuals in the candidate’s life such as parents, or any existing minor children, will have an impact on the success or failure of the process and the aftermath of conversion.
Sounds much more like a "be prepared for some difficult conversations" than a slam-the-door.
(It is true that halacha views a new convert as no one's relative per se from a technical standpoint; that's different.)
I will take it a step further, in light of Rabbi Feinstein's nuances on this very topic, and say the sever-everything position is ... well perhaps someone misunderstood, or it was only intended in particular circumstances.
Rabbi Moshe Feinstein's responsum YD2:130, summer 1962, to Rabbi Samuel Yalow of Syracuse -- an adult convert who hasn't visited her non-Jewish mother for years, and now wants to do so as her mom is ailing.
In conclusion: even without the illness, she was allowed to occasionally visit, if not doing so would have been seen as ungrateful; but to be a regular visitor would be prohibited, to prevent sliding back from Judaism. [The convert's] children certainly shouldn't get used to going there, as they may serve them non-kosher. But now that the non-Jewish mother is ailing -- besides the fact that we are obligated to tend to sick non-Jews too -- she is obligated to go visit her, with the children, as a small amount of honor for parents vs. disgrace, as Maimonides wrote [befits the non-Jewish parents of converts] and is ruled as such in Shulchan Aruch.
Rabbi Feinstein's secretary records similar missives in Mesoras Moshe Volume II, pages 265--266:
Must a convert distance from his non-Jewish family
... a sincere convert who cried as someone had told her to distance herself completely from her parents -- [Rabbi Feinstein said] that's not what she was actually obligated to do. As Maimonides says he must honor them somewhat, out of gratitude ... once Maimonides introduces the concept of honor, to plain-out sever and decree they can't meet at all is tremendous wickedness. [Rish'us gedolah!]
... In this particular case, the parents were in England ... the whole point of distancing was to prevent any concern that they'd influence her to return to her old life ... the rabbi advised that she go visit once a year, bring her [Jewish] husband, and stay at a hotel, not her parents' house.
Another time, the rabbi answered that a non-Jewish grandfather could be addressed as Sabba or "grandfather", just be careful to only visit him every so often [b'akrai], with the same explanation as listed above.
The rabbi told Rabbi Twersky of Denver to tell converts that they should visit their non-Jewish parents several times a year -- while we don't want too much closeness, don't distance them to the point of "disgrace", which Maimonides prohibited ...