For many families, religious beliefs are some of the most deeply held tenants of their lives, and it's normally taken for granted that children will grow up in the religion of their parents. However, if the parents are divorced or were never married and subscribe to different religions, it can make this much more complicated.
Some parents have an informal agreement that the child will be exposed to both religions during parenting time with that parent, but when a divorce happens or a separation turns nasty, these agreements often sour as well. Having a formal legal agreement outlining the children's religious education as well as if or how the children will be exposed to the beliefs and practices can reduce arguments on this matter and move things back into the realm of civility.
In the majority of these cases, the courts uphold the parents' rights to religious freedom and to bring their children up in the way they see fit. The courts commonly make a provision in the divorce decree or shared parenting agreement that the child can be exposed to both religions. The exception to this is when one parent argues that exposure to a religion results in harm to the child.
If this is your situation, it is best to talk with a family law attorney as soon as possible, regardless of which side of the courtroom you are standing on. These cases can be very complicated, and it's common for communication in other parenting areas to breakdown while the court is hearing evidence and making its decision.
Source: FindLaw, "Divorce: Child Custody and Religion," accessed Aug. 13, 2015