I can't quote you any specific set of details, but being a former Earthlink user I can say that Earthlink uses a spam blocking routine that can be set to various levels. When an unknown user sends an Email to an Earthlink user who has this protection enabled, the sender of the Email receives a notice back that they need to fill out a special form that then gets sent back to the Earthlink customer identifying the sender.
The idea behind this is that every Email is considered junk mail unless the sender is identified. The best solution would be to contact those in the ward/stake who use Earthlink and ask that they add your Email address to their list of accepted Email addresses. You might also post a brief notice on the ward bulletin boards advising members of the problem and giving them your Email address. If your notice contained some urging telling them that they are missing out on important announcements about ward/stake activities, it might carry more weight.
The other option you already mentioned would be to have them set up a special Gmail, or other free account, which I agree would probably never get used.
I have been away from Earthlink (too expensive) for a few years and it's possible that they have added something else that I'm not aware of. But, this is how it used to work.