I saw this in a new sefer from R Itamar Garbuz, a gaon בלי גוזמא. I added a few words at the end.
שמות ט ו-ז
ויעש יהוה את הדבר הזה ממחרת וימת כל מקנה מצרים וממקנה בני־ישראל לא מת אחד
וישלח פרעה והנה לא מת ממקנה ישראל עד אחד ויכבד לב פרעה ולא שלח את־העם
מלבי"ם
והנה לא מת ממקנה ישראל עד אחד. במ"ש לקמן (יד כח) לא נשאר בהם עד אחד פי' חז"ל שפרעה נשאר, ר"ל שפי' עד ולא עד בכלל שאחד נשאר, וכן במ"ש שופטים (ד טז) לא נשאר עד אחד נשאר סיסרא, ומשמע שגם פה מת אחד, וי"ל שהיה בהמת בן האשה הישראלית והוא בן איש מצרי, שבדיני ישראל היה כמצרי, כמש"ש במקומו, ופרעה חשב שהוא מישראל וכיון שבהמתו מתה לא נתקיים דבר משה ועי"כ ויכבד לב פרעה:
The same is said in the name of the Gaon.
(והובא בשם הגר"א ב'דער תורה – קוואל' מר' אלכסנדר זושא פרידמאן על הפסוק 'וממקנה בני ישראל' הוצאת ווורשא שנת תרח"צ).
The reason we saw him as a Mitzri is because of the shitta of the חכמי הצרפתים brought in the Ramban in the parsha of the Mekaleil (ויקרא כ"ד י) that before Mattan Torah a child of a Jewish woman and a non-Jewish man is not a Jew. The rule that you go by the mother was only after Mattan Torah.
Ramban:
וְטַעַם "בֶּן הַיִּשְׂרְאֵלִית וְאִישׁ הַיִּשְׂרְאֵלִי", לְהוֹרוֹת כִּי הַגּוֹי הַבָּא עַל בַּת יִשְׂרָאֵל הַוָּלָד אֵינוֹ יִשְׂרְאֵלִי. וְאע"פ שֶׁפָּסַקְנוּ בַּגְּמָרָא (יבמות מה) דְּגוֹי הַבָּא עַל בַּת יִשְׂרָאֵל הַוָּלָד כָּשֵׁר בֵּין בִּפְנוּיָה בֵּין בְּאֵשֶׁת אִישׁ, הֲרֵי אָמְרוּ (בכורות מז), מְזַהֲמִין אֶת הַוָּלָד, לוֹמַר שֶׁהוּא פָּגוּם לַכְּהֻנָּה וְכָל שֶׁכֵּן שֶׁאֵינוֹ יִשְׂרְאֵלִי בִּשְׁמוֹ לְעִנְיַן הַיַּחַס בַּדְּגָלִים וּבְנַחֲלַת הָאָרֶץ, כִּי "לִשְׁמוֹת מַטּוֹת אֲבֹתָם" כָּתוּב בָּהֶן (במדבר כו נה). וּמַה שֶׁאָמַר בְּת"כ (פרשה יד א), "בְּתוֹךְ בְּנֵי יִשְׂרָאֵל", מְלַמֵּד שֶׁנִּתְגַּיֵּר, אֵינוֹ שֶׁיִּצְטָרֵךְ בְּגֵרוּת אֶלָּא כְּכָל יִשְׂרָאֵל שֶׁנִּכְנְסוּ לַבְּרִית בְּמִילָה וּטְבִילָה וְהַרְצָאַת דָּמִים בִּשְׁעַת מַתַּן תּוֹרָה (כריתות ט), אֲבָל נִתְכַּוְּנוּ לוֹמַר שֶׁהָלַךְ אַחֲרֵי אִמּוֹ וְנִדְבַּק בְּיִשְׂרָאֵל. וְזֶה טַעַם "בְּתוֹךְ בְּנֵי יִשְׂרָאֵל", שֶׁהָיָה עִמָּהֶם וְלֹא רָצָה לָלֶכֶת אַחֲרֵי אָבִיו לִהְיוֹת מִצְרִי. וְכֵן מַה שֶׁאָמְרוּ בְּת"כ (שם), אע"פ שֶׁלֹּא הָיוּ מַמְזֵרִים בְּאוֹתָהּ שָׁעָה הוּא הָיָה כְּמַמְזֵר, כְּדִבְרֵי יָחִיד הִיא שְׁנוּיָה, וַהֲלָכָה הַוָּלָד כָּשֵׁר. וְהַצָּרְפָתִים אוֹמְרִים כִּי טַעַם הַגֵּרוּת מִפְּנֵי שֶׁהָיָה קֹדֶם מַתַּן תּוֹרָה, וְהָיָה מִשְׁפָּטוֹ לֵילֵךְ אַחַר הַזָּכָר, מִמַּה שֶׁאָמְרוּ (יבמות עח), בָּאֻמּוֹת הַלֵּךְ אַחַר הַזָּכָר, וְכַאֲשֶׁר נוֹלַד זֶה לֹא מָלוּ אוֹתוֹ, כִּי מִצְרִי הָיָה בְּדִינוֹ, אֲבָל כְּשֶׁגָּדַל נִתְגַּיֵּר לְדַעְתּוֹ וְנִמּוֹל. וְאֵין דַּעְתִּי כָּךְ, כִּי מֵעֵת שֶׁבָּא אַבְרָהָם בַּבְּרִית הָיוּ יִשְׂרָאֵל וּבַגּוֹיִם לֹא יִתְחַשָּׁבוּ, וּכְמוֹ שֶׁאָמַר בְּעֵשָׂו (קידושין יח), וְדִלְמָא יִשְׂרָאֵל מְשֻׁמָּד שָׁאנֵי, וְק"ו הַדָּבָר, אִם לְאַחַר מַתַּן תּוֹרָה שֶׁהַגּוֹי הַבָּא עַל בַּת אַבְרָהָם מֵחַיָּבֵי לָאוִין וְאֵין לוֹ בָּהּ קִדּוּשִׁין, הִיא מִקְוֶה טַהֲרָה לָאֻמּוֹת לְהַכְשִׁיר אֶת וְלָדָהּ לִהְיוֹת כָּמוֹהָ, לֹא כָל שֶׁכֵּן קֹדֶם הַתּוֹרָה, שֶׁתְּהֵא מְטַהֶרֶת וְלָדָהּ לִהְיוֹת כָּמוֹהָ, לְחַיְּבוֹ בְּמִילָה כְּזַרְעוֹ שֶׁל אַבְרָהָם וְיִהְיֶה מִכְּלַל בְּנֵי יִשְׂרָאֵל:
Pharaoh, however, saw him as a Jew. Since one Jew's animal died, Pharaoh decided it proved that Moshe's words (ט:ד)
וְהִפְלָה יְהֹוָה בֵּין מִקְנֵה יִשְׂרָאֵל וּבֵין מִקְנֵה מִצְרָיִם וְלֹא יָמוּת מִכׇּל־לִבְנֵי יִשְׂרָאֵל דָּבָר׃
were not fulfilled, because one had died, this was not an act of God, which would have been perfect, but mere magic and curses, which are imperfect.
The kashe they ask on the Chachmei HaTzarkatim is that in Yevamos 100b it says Hashem told Avraham, do not marry an akum or shifcha, because then your child will follow her halachic status.
דִּכְתִיב: ״לִהְיוֹת לְךָ לֵאלֹהִים וּלְזַרְעֲךָ אַחֲרֶיךָ״, הָתָם מַאי קָא מַזְהַר לֵיהּ רַחֲמָנָא? הָכִי קָאָמַר לֵיהּ: לָא תִּנְסַב גּוֹיָה וְשִׁפְחָה, דְּלָא לֵיזִיל זַרְעָךְ בָּתְרַהּ.
This contradicts shittas Chachmei HaTzarfatim.
Harav Garbuz answers that maybe their shitta is that before Mattan Torah the child is viewed as partially each; or maybe it is only lechumra that we go after the father, but lechumra we would go after the mother as well.
But, he asks, if so, why would his animal die? The Medrash here says clearly that an animal owned in partnership of a goy and a Yisrael did not die!
He answers that this is only true for an animal owned half by a Jew and half by a Goy. It does not apply to an animal owned entirely by a half Jew-half Goy.
But then he says that the kashe from Yevamos is not a kashe at all. The pshat in the Chachmei HaTzarfatim is that before Mattan Torah, the din Yisroel was complete, but the din Akum was complete. So of course the mother is dominant in determining whether you are a Jew. But where the mother is a semi-Yisrael and the father is an akum gamur, of course you go after the father. After Mattan Torah, when the din Yisrael is גמור, of course you go after the mother. But if it were a non-Jewish mother and a Jewish father, or course we would not go after the father! We would certainly go after the mother who is A the mother, and B a goyah gemura. And that is why the RBSO told Avraham, don't marry a non-Jewish woman, because even the Chachmei HaTzarfatim would agree the child would be a goy.
(I always assumed that the Chachmei HaTzarfatim was based on Yevamos 78b that among the nations you go by the father, such as a Knaani father with a Spanish mother, there's a din of lo sechayeh, but a Spanish father and a Knaani mother, the child is fine. This would not work with R Garbuz's mehalach.)
Back to the basic halacha of עכו"ם ועבד הבא על בת ישראל.
The Gemara paskens that הולד כשר. Tosfos says this means he is a kosher goy and not a Yisrael mamzer, and he needs real geirus. But the Rambam and the Mechaber pasken it means he is a Yisrael kasher and does not need geirus, that we simply ignore the father and go after the mother. The Chazon Ish (Eh end of siman 6) says this is the halacha with no safek at all.
But Tshuvos Chemdas Shlomo (EH 2) brings a tshuva from the Nesivos that le'halacha the child needs geirus. See also RAE Gilyon YD 266:12 who discusses whether you can be mal this child on Shabbos.
He says that he heard from Rav Shach that someone asked his uncle, Reb Isser Zalman, what he would do in such a case, considering the shitta of RAE and the Nesivos. RIZ answered that Klal Yisrael paskened; it is a הוראה המקובלת, and as such, can not be questioned.
I am just adding that it is well known that Reb Moshe held, as did the Maharit Algazi, that the halachic status of the child depends on how he was raised. If he was raised a Jew, he is a ישראל גמור. If he was raised as a goy, he is an עכו"ם גמור. (See Avi Ezri Issurei Biah 15:3 where he brings the Maharit and says this idea is completely incomprehensible and should be stricken from the record and never heard again. He did not know that the Marshal holds exactly like that, besides Reb Moshe. It is the Mahrshal, the Maharit Algazi, and Reb Moshe. Try striking that from the record.)
When I said this over, R Dr Gary Schreiber asked me that according to the Chachmei Hatzarfatim, the מקלל should have died at Makkas Bechoros. I tried to answer that this was to prevent chillul Hashem, but that's a weak answer, because why wasn't that a cheshbon at Makkas Dever. You could say that it wasn't so important that Pharaoh be nispoel from dever, because Hashem still wanted to bring four more makkos, but it's shvach. Unless the pshat is that he was not a bechor to his father, and even if he was a bechor to his mother, his mother was Jewish.
Reb Moish Pollack pointed out that I should be ashamed of myself for not remembering a Rashi right here in 12:13;
ולא יהיה בכם נגף. אבל הוה הוא במצרים. הרי שהיה מצרי בביתו של ישראל, יכול ימלט? ת"ל "ולא יהיה בכם נגף", אבל הוה במצרים שבבתיכם. הרי שהיה ישראל בביתו של מצרי, שומע אני ילקה כמותו, ת"ל "ולא יהיה בכם נגף" (מכילתא):
He is right.
From Shasdaf's hearos, it seems that we can resolve the problem I had with the Mechilta. If, as the Mechilta says, a Jew in the street was safe, and a Mitzri in a Jewish house would die, what does it mean that Hashem was posei'ach on the houses with Dam? Does it mean that since the majority of Jews put dam on the house, it protected even "עם שבשדות?" But it could be, according to the many rishonim and achronim who hold that the din עכו"ם ועבד הבא על בת ישראל הולד כשר, and the idea that before mattan Torah you would go after the father, is not all or none, and such a child, before or after mattan Torah, would have some dinim of Yisrael and some dinim of גוי. If so, it's very simple. For a Yisrael, it did not matter if you were inside or outside the house. For a Goy, it also did not matter. But for a חצי חצי person, inside the house was safe and outside the house was dangerous.
I think this is a good thing to add to the seder oeuvre.
👉In the comments, Shasdaf made it clear that he does not like it when I edit posts to reflect comments or new thinking. I responded that I very much appreciate his point, and that is why I edited to post to include his he'ara.