Prophet Mohammed (peace be upon him and his progeny) is the final prophet, and his message is the last divine message. Practices of other religions are not recognized by the Islamic Sharia. However, Islam emphasizes on cohabitation with followers of other religions. It is permissible to do what makes such co-existence without considering such acts a part of the Sharia, as long as it does not involve any forbidden act.
Your fasting is void and you should make up that day. If you knew that the time of fasting had began and still broke the fast then you should pay Kaffara as well.
If fasting harms the woman who is breastfeeding by greatly decreasing her milk, or stopping its flow, then it is permissible for her not to fast. She should make up the missed fasts before the next Ramadan. Furthermore, a sum of 900 grams of food like wheat, oat and rice must be paid to the needy believers for each missed day.
