Thank you very much to all for the detailed comments. I appreciate you keeping advice simple enough for someone like me, who decades ago counted as a "power user" of PCs, but who has no particular technical training or computer-related work experience. I will have to digest some of this advice for women (they are mostly women in the local group) who are barely comfortable using Facebook. And I'll pass on other tips to the women and men who have actual technical backgrounds and will be implementing the different online projects of the local group.
Advice that especially fits our situation is having an appropriate level of security for an intentionally PUBLIC organization whose members will be identifiable by multiple in-person activities in public places over the next few years. We are not afraid to be known as people who support the cause that we support. We are resolutely sticking to peaceful, legal means to reach our goals. Many group members are VERY wary of new group members--plenty of them are wary of me--so we will have to build mutual trust as we build mutual communication and public-facing communication. I like mz's advice to remind members that anything they say in an online group--even in our internal online groups for members only--might show up in mass media or in propaganda spread by opponents, so I try to model careful speaking and writing.
I'll link here to a document about the bad-case scenario of living under an actual dictatorship with a secret police force that kills political opponents. That's something I've actually done (in Taiwan, in the 1980s). The good news is that nonviolent popular movements can even overthrow dictators and establish democratic republics with full protection of civil liberties. That takes mental toughness, but it can be done. I've seen it done. You may be inspired by the document linked here and the other documents (in numerous languages) posted at the same website.
http://www.aeinstein.org/wp-content/uploads/2013/09/FDTD.pdf