Coincidentally, I saw a remarkable idea this week. We are all familiar with the rule of matrilineal descent (Kiddushin 68b and Yerushalmi Kiddusin 3:12 and Bamidbar Rabba 19:3), that Jewish identity descends through the Jewish mother. If a non-Jewish man fathers a child with a Jewish woman, the child is Jewish. (This was not necessarily true prior to Sinai- see Ramban Vayikra 24:10- but that is not the topic of this discussion.)
There might be two major exceptions, or caveats, involving this rule. They are minority opinions: neither is widely accepted.
1. The Mahrshal in Yevamot 16b and the Maharit Algazi in Bechoros 47a. They hold that such a child is only Jewish if he/she was raised as a Jew, i.e., that he/she conducted him/herself as a Jew. Once the Jewish identity vests, it is, of course, permanent.
2. There is one Achron that holds, or at least, proposes, that the child of a Jewish mother and gentile father is Jewish only after the child is born. During pregnancy, the fetus is not Jewish. The child only becomes Jewish at birth.
This is the opinion of Rav Eliahu Poisek (A Ukrainian Rov, see end of post, in his Marbeh Torah on Hilchos Ribbis, end of Siman 159). It is brought down in the Darkei Teshuva there in Yoreh Dei'ah. It can be seen here. This is what he says:
(This would generate numerous halachic ramifications. Examples: Ribbis to and from his estate; piku'ach nefesh; whether he can be yoreish at that point; and, most importantly, how many chickens you 'd need for kaparos.)
This is obviously only one Rov's opinion, and would not constitute citation to authority. In fact, it's not in the sefer that he says he said it in, his כורת הברית, and I think he regretted saying it and took it out. But I have another surprise for you. You will see that although Rav Poisek is the only person to say this explicitly, it is clear that there are others that will find themselves painted into the corner with him.
There are Achronim that hold that during pregnancy, the mother is not legally denominated as "mother" of the fetus, but the father is called the "father" as soon as the pregnancy becomes evident. I'll bet dollars to donuts that these Achronim didn't realize it, but it seems to me that if you accept their svara, then the chiddush of Reb Eliahu Posek is concomitant. Although the mother's religious identity is dominant over that of the father, that's only once the woman is called the child's mother. According to these Achronim, during pregnancy there is no legal mother, only a father. If the father is a goy, then of course the child is a goy. But once the child is born, and he has a mother and a father, then the mother's religious identity is absolutely determinative.
(I realize that אפקריה רחמנא לזרעיה, Yevamos 98a. But I don't need for the עובר to be misyacheis to the father to make him a goy. All I need is that he's not misyacheis to a father who is a Yisrael. If he has no yichus to a Yisrael father, and he has no mother l'halacha, then by default, he's a non-Jew.)
And who, you ask, are these Achronim? Are they mischievous Poilishe Pilpul People? Or obscure Ukrainian Rabbanim? Nope. They are Reb Yosef Engel and Dayan Fisher.
Reb Yosef Engel is in his Beis Ha'Otzer, Klal 4, Av, and it can be found here. Dayan Fisher is in his Even Yisrael on the Rambam in 16 Ishus 7, and can be found here, in the third paragraph.
If you think about it, you'll realize that the Maharshal wouldn't be shocked, either. If the status of such a child is only fixed if he is raised/acts as a Jew, then there must be a period of pendancy. His status is to be later determined- at which point his status is retroactive. Perhaps it's only retroactive to the moment of birth, but not to the moment of conception.
And if you take this to its natural conclusion, what about a Jewish man who fathers a child by a non-Jewish woman? Would these poskim say that during the pregnancy the fetus is Jewish, and only becomes non-Jewish when it's born?
Anything can happen on Torah Avenue.
Because this is the internet age, and you can find out all different kinds of things about all different kinds of people, here's a paragraph from the Wikipedia article about the Posek family, evidently written by a family member.