Why don't you carry on phoning them once a week and assume that's what they meant by limited family business? If it isn't what they meant they'll have to tell you. As you want to keep contact with them why not do that? You don't have to talk about religion, you don't anyway I'm sure.
My siblings have shunned me for over thirty years, but if I want to contact them if I hear of a serious illness or a death I contact them. I'm not the one shunning, I'm not being obedient to a stupid cult. As your dad asks you not to phone immediately and talk about religion, fine, but why give up your weekly phone call? You're over fifty hears old, who you phone is your choice. Good luck, I know how hard this is believe me.