It sounds as though this family member is becoming involved in neopaganism, a movement within the New Age that seeks to revive ancient religions. These include witchcraft, magick, goddess worship, shamanism, Celtic spirituality and Native American spirituality. Most of these are animistic, occult centered practices.
Although he probably won't want to hear it, the Native American spirituality he's dabbling in is such a gross distortion of authentic Native American spirituality that the Lakota tribes actually issued a declaration of war against New Agers (they call them "Plastic Shamans") for co-opting their sacred beliefs. The perfect example is the so-called Native American tarot cards. Indians don't use tarot cards! They never have and they never will. New Agers have done the same thing with the medicine wheel (they make them into earrings and keychains, which is highly offensive to the Indians) vision quests, and sweat lodges.
(For an expose of how deadly some of these New Age distortions can be, read my post about the three people who died in a sweat lodge ceremony orchestrated by New Age guru James Ray.)
This is also where he's getting the "two spirit" idea, which refers to a male transvestite indian (known as a berdache) who performs female duties in a tribe. This person can be either hetero- or homosexual.
All of this is nothing more than a money-making scheme that is causing great pain and offense to Native Americans - and also deceiving many good souls away from the Truth, such as your family member.
However, I do see a bright spot in all this. One reason why this family member doesn't want to talk with you could be that the Holy Spirit convicted him of his sin when he read your letter. Hostility can be a sign that this conviction has taken place which is a good sign in spite of how it might feel! It means the person can at least still hear the voice of the Spirit speaking from within.
The first thing I would do is become a prayer warrior on his behalf. Offer Masses for him, pray the Rosary for him, ask Jesus to give him the grace to stop opening the door to the occult. This is a very important prayer to make on his behalf because whenever people seek knowledge through divination, they open a door, and every time that door opens, it gets harder and harder to close.
But what really concerns me is that he thinks God is telling him to be a homosexual. This is the devil telling him this, not Jesus Christ, but because this person doesn't know Jesus very well, he is unable to discern the real Jesus from an imposter. Very dangerous position to be in when you're dabbling around in the occult!
My Learn to Discern Compendium: Is it Christian or New Age contains a chapter on magick that explains what happens to people who think they're using occult powers for their own needs. In the end, these occult forces are using them and many of these people must be delivered by a priest in order to get rid of these tormenting spirits. It doesn't sound like he's too open to hearing the truth right now, but you might consider keeping it around just in case.
As for you, don't give up your peace. That will only "score another point" for the devil. Remember, the Holy Spirit prompted you to write the letter, and He knew how this family member would react. You did what was asked of you. If He needs you to do something else, stay open to His suggestions. Until then, pray for this family member and leave the rest in God's hands.
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