Organ and tissue donation are NOT the same thing! Less than 1% of people who die qualify to be organ donors. However, LOTS of people qualify to be bone or tissue donors. You can be one or both. In Alabama, you can agree when you get your driver's license renewed and/or sign up online!
The major organs that can be transplanted are heart, lung, liver, kidneys, pancreas, and intestines.
Tissues that can be donated include corneas, muscle, skin, and bone. There are lots of different parts of these, but since I am not yet a fluent speaker of medical, just trust me on this one!
NO major world religion objects to organ donation. Many will not come out and say "yes, you should donate" in some sort of official statement (although there are some that do!), but all acknowledge it as a generous and self-less act of compassion towards others.
Legally, in many states, your next of kin does NOT have to consent to donation if you have signed the equivalent of an advance directive (a donor card, driver's license, or online register). However, in Alabama as well as some other states, if your family objects the doctors will not go against the wishes of your family so it is STILL important to have those conversations with your family if you wish to be a donor. This isn't the case in all states and some states will go against the wishes of your family if you have agreed but they object.
Your will not receive sub-standard care if you are a donor so that someone can take your organs. If you or your family do make the decision to donate, there is no cost to your or your family. Donation should not delay any preparations for a funeral.