Will you please provide more information. I have no idea what you activated. Was this an addon?

I received two messages from Moveon.org with the same content but with different headers.

The first header: From reply@petitions.moveon.org [via Relay] To (my name) Reply to replies@relay.firefox.com

Note [via Relay] in the From line and [@relay.firefox.com] in the Reply to line. Using Relay apparently substitutes an email address in the reply other than my own for security purposes.

The second header (Relay wasn't in the message): From Demand Progress <reply@petitions.moveon.org> To (my name) Reply to Demand Progress <info@demandprogress.org>

Note: In the second header my name and email address are legible in the reply.

You need to remove the alias email you created via Firefox Relay from your moveon.org account.