My sister married a Muslim and converted. We live in cities several hours apart, but the family comes together for Thanksgiving, and I have brought birthday gifts for her children in years past.
I sent my sister an e-mail this year asking for gift suggestions, and she told me to not buy them anything because they celebrated two Eid holidays this fall, which is when they exchange gifts in their religion. She wanted the Eid holidays to remain extra special and the children not to become spoiled with too many gifts.
Growing up, the "gift" days for children in our family were Christmas and birthdays. The passing of each of these events seemingly works as another step in feeling distance and disconnect from the children.
Is there anything I can do on their birthdays to show them their non-Muslim family loves them enough to buy them gifts too, without offending my sister's wishes?
Answer: You're losing a gift-giving opportunity to religion.
If you want to lose your family to religion, the best way to accomplish that is to rage, rage against the dying of your traditions, instead of adapting to theirs.
Have you ever asked to be included in their Eid celebrations?
I understand your frustration at being denied the chance to spoil your nieces and nephews. But it couldn't hurt to consider that spoiling with material gifts is overrated.
Ask your sister about their interests versus gift ideas, and you'll probably get a more satisfying answer. Feed those interests, versus their toy chests, and you'll probably see more than once-a-year joy on their faces.