Suppose a man wants to convert to Judaism but cannot have a circumcision for bio-medical reasons (he has a foreskin, but has hemophilia or some other condition which would make the surgery fatal or life-threatening. Does this prevent him from converting, or may he complete the conversion process without being circumcised?
There is a general consensus among the poskim that one who has an orlah cannot convert without having a milah. See here who refers to the views of:
שו״ת ארץ טובה סי׳ ב׳, ומשברי ים סי׳ ט״ו, זכר זכר יצחק סי׳ ג׳, מלמד להועיל סי׳ פ״ו, דעת כהן סי׳ ק״נ, ועיין בשרידי אש ח״ב סי׳ ק״ב־ק״ג שכתב שלתשובתו הסכימו כל גדולי הדור,ובכללם מרן הגאון רח״ע גדודזנסקי זצ״ל.
This is also the opinion of R. Tzvi Pesach Frank, הר צבי יורה דעה סי' רכ.
Like everything else, it's debated!
There are opinions that he simply can't convert, that he needs no circumcision, or that he is allowed to "roll the dice" and choose to risk circumcision (let's assume a hemophiliac) for the sake of becoming Jewish. (If I'm not mistaken, it's mentioned in this shiur.)
The best bet would be to see what drugs and techniques could be used to make circumcision possible without being life-threatening.