Well, these things get complicated; and I had a personal reason for wondering if Christians in general have any clear consensus on what should determine the religion of the child.
My mother was Catholic, my father raised Episcopalian. He refused to become Catholic, but agreed when they married that I would be raised Catholic; so I was baptized.
Later, they divorced; I was basically raised by my father and his mother, and grew up in the Presbyterian church.
A Catholic woman in the neighborhood somehow found out that I’d been baptized Catholic (I guess because she was a member of the Church that baptized me) and knew that I was not ultimately raised in the Church; and she told me (a child of about 7 years old) that there was a ‘curse’ on me because of this.
(I’d been raised better than to let something like that bother me; but it did make me wonder about *people*, and about religion.)
Again, these things get complicated.
Ironically, I too have an Episcopalian father and my mother now deceased was Catholic. My father agreed that I could be raised Catholic, and he signed the paper I mentioned. It was never an issue because my parents remained married until my mother died when I was 17, and by that point I was confirmed Catholic and still am a practicing Catholic. I would however attend my father’s church as well especially on liturgical holy days so we could be together. I love my faith and am thankful to be a member of the Catholic church,.
The woman who told you you are cursed is a mean woman who incidentally is just plain wrong, and had little understanding of her faith. The Catholic Church recognizes baptisms from other Christian denominations, and considers you to be a fellow Christian. I hope that helps a bit. These things are complicated.. God Bless You.