Religion and faith are two different things. One can have faith without having a religion, but one cannot have a religion without subscribing to a faith. Christianity is a faith, Christendom is the religion. Religions have man-made rules and traditions, while faith is simply the faith in a deity and that deity’s instructions (in Christianity, this is the Bible).
There are several areas of Christendom, ‘normal’ Christians- Apostolic, Baptist, etc; Mormons (Latter Day Saints), and Jehovah’s Witnesses all claim Jesus Christ as their Savior. While ‘normal’ Christians use the Bible, as do Jehovah’s Witnesses, Mormons have the Book of Mormon, which is slightly different. The faith is the same, but the religion is different.
By converting yourself to Christianity, you are not dooming your parents to Hell. They are adults and can account for their own behavior and choices. If God is real, they will be left to His judgment come that day. If God is not real, they lived lives of generosity for the sake of generosity.
Although the Bible does give us direct instructions and rules, God has always said that He will choose who enters His gates, and none shall judge another before Him. No man will ever know the fate of another, because only God has that power. Even the righteous shall scarcely make it.
If you believe in God, believe in Him. It is fully up to you. I know, as a believer, it is sometimes very hard to think that our friends and family may not end up in Heaven, but truly, we don’t even know if we will. The best thing to do is what feels right for you, and hope for the best.
