Today I got my Halachic Organ Donor Society card. (I have a regular one and am on the NHS registry as well.)
Although I'm not strictly observant, I wanted this for a reason. While Neil would have no problem with donating my organs, my family would. Jews are traditionally very reluctant to donate organs, for several reasons:
1) Judaism prescribes utter respect for the dead and forbids desecrating a corpse. Many people erroneously believe that organ donation is desecration. (Rabbis have ruled that pikuach nefesh, saving a life, overrules this consideration.) This is why Jews rarely permit autopsies.
2) People believe that this will prevent you being resurrected when the Messiah comes. (Also untrue--as is obvious if you think about it. Surely God can replace your kidneys?)
3) For observant Jews, there's also the issue over time of death, and whether halachic (Jewish religious) death corresponds with brain death. The Chief Rabbinate of Israel has ruled it does, and so all organs can be transplanted. If death is only cessation of heartbeat, most organs can't be donated.
For my family, it would primarily be the first issue--it's simply become a huge taboo. By carrying a HODS card, I'm sending the message that this is religiously acceptable, and hopefully easing any objections my family might have.