I'm not aware of any religions affiliated with the International Red Cross, though you're welcome to educate me. I suppose it will end when sovereign nations cease using the symbols of "new religions".
BTW, a clue as to why the MDA uses that symbol.
As you may have read, the Red Cross came from the Swiss flag inverted, not as a religious organization. Then the Muslims want their own because they don't like the cross. Now the Jews want their own as an official part of the Red Cross. Next the [insert religion here]. The Red Cross was good enough with just the cross.
No slight intended against the great work of Magen David Adom.
[I'm not aware of any religions affiliated with the International Red Cross]
I believe the Red Crescent is already.
[ The red crescent, along with the Red Lion and Sun of Iran, was enshrined with the red cross in the Geneva conventions of 1929.]
Is the Red Cross really trustworthy? I have read on two occasions that they kept donated monies for their own use and that they have a checkered past being closer to some of America's enemies than to us.