As someone who works for a nonprofit, we have volunteers and donors that work in many different functions. Some are hands-on, some send money, some speak at fundraising events, some actively recruit other donors, etc. No agency should reasonably expect that there is a one size fits all way for people to help out.

I would suggest using whichever means you are most comfortable with (e-mail, phone--even if you call late to leave a voicemail--or in person) and let them know that while you value the mission of the agency greatly, and would like to remain active in this cause, your current level of engagement is what you are comfortable with and what you are able to commit to at this time. Then don't budge. You have the right to participate at whatever level suits you, and they should be grateful for it. You don't need to explain that it's anxiety that prevents you from going further. That isn't really their business.

Should you like to work on your anxiety, there are support groups and counseling that you could benefit from. It is a difficult thing to work on, as you know, because it is a cycle, and it's hard to get started specifically because that's part of the problem. But, don't stress yourself out. You've stepped out into the world to aid a cause you believe in, and you should be commended for that. You've done what you know to be your best, and that's more than most people ever do.

If you have someone to recommend to them (as in "you know, I don't think I can commit to being a speaker at the event, but so-and-so is really amazing, and I have their number..."), then great. If not, just state your boundaries firmly, thank them for their enthusiasm, and let it go.