@JPB,
No my suggestion would be to
fake your belief, if belief is going to be imposed on you. Both parties are viewing baptism as more important than the life (or well-being) of a child.
I believe 1st Kings is canonical to both religions involved.
A part of the story involving the dispute over who is the parent of a child:
כב וַתֹּאמֶר הָאִשָּׁה הָאַחֶרֶת לֹא כִי, בְּנִי הַחַי וּבְנֵךְ הַמֵּת, וְזֹאת אֹמֶרֶת לֹא כִי, בְּנֵךְ הַמֵּת וּבְנִי הֶחָי; וַתְּדַבֵּרְנָה, לִפְנֵי הַמֶּלֶךְ. 22 And the other woman said: 'Nay; but the living is my son, and the dead is thy son.' And this said: 'No; but the dead is thy son, and the living is my son.' Thus they spoke before the king.
כג וַיֹּאמֶר הַמֶּלֶךְ--זֹאת אֹמֶרֶת, זֶה-בְּנִי הַחַי וּבְנֵךְ הַמֵּת; וְזֹאת אֹמֶרֶת לֹא כִי, בְּנֵךְ הַמֵּת וּבְנִי הֶחָי. {פ} 23 Then said the king: 'The one saith: This is my son that liveth, and thy son is the dead; and the other saith: Nay; but thy son is the dead, and my son is the living.'
כד וַיֹּאמֶר הַמֶּלֶךְ, קְחוּ לִי-חָרֶב; וַיָּבִאוּ הַחֶרֶב, לִפְנֵי הַמֶּלֶךְ. 24 And the king said: 'Fetch me a sword.' And they brought a sword before the king.
כה וַיֹּאמֶר הַמֶּלֶךְ, גִּזְרוּ אֶת-הַיֶּלֶד הַחַי לִשְׁנָיִם; וּתְנוּ אֶת-הַחֲצִי לְאַחַת, וְאֶת-הַחֲצִי לְאֶחָת. 25 And the king said: 'Divide the living child in two, and give half to the one, and half to the other.'
כו וַתֹּאמֶר הָאִשָּׁה אֲשֶׁר-בְּנָהּ הַחַי אֶל-הַמֶּלֶךְ, כִּי-נִכְמְרוּ רַחֲמֶיהָ עַל-בְּנָהּ, וַתֹּאמֶר בִּי אֲדֹנִי תְּנוּ-לָהּ אֶת-הַיָּלוּד הַחַי, וְהָמֵת אַל-תְּמִיתֻהוּ; וְזֹאת אֹמֶרֶת, גַּם-לִי גַם-לָךְ לֹא יִהְיֶה--גְּזֹרוּ. 26 Then spoke the woman whose the living child was unto the king, for her heart yearned upon her son, and she said: 'Oh, my lord, give her the living child, and in no wise slay it.' But the other said: 'It shall be neither mine nor thine; divide it.'
כז וַיַּעַן הַמֶּלֶךְ וַיֹּאמֶר, תְּנוּ-לָהּ אֶת-הַיָּלוּד הַחַי, וְהָמֵת, לֹא תְמִיתֻהוּ: הִיא, אִמּוֹ. {ס} 27 Then the king answered and said: 'Give her the living child, and in no wise slay it: she is the mother thereof.'
If you are willing to tear a child or a child's well-being in half, then I doubt your true concern for the child.
[
I am not religious by the way, I simply have studied other religions]
I may certainly be in disagreement with some priests and rabbis, but I doubt many (of either) are in disagreement with this.