Appelbaum, a well-known privacy advocate and developer, left the project, a system enabling anonymous online communication, on 2 June after charges of sexual misconduct were raised against him.
Those calling for the strike want users to avoid the network, those running nodes to shut them down and are asking developers not to work on Tor software for the period of the strike.
"A short blackout may hurt in the short term, but save Tor in the long term. It will also allow dissenting voices to be heard."
This group is calling for the executive director of the project, Shari Steele, to step down. It also wants president and co-founder Roger Dingledine to leave because he allegedly handled the Appelbaum affair in "a partial and unprofessional manner".
There are a total of 10 demands made regarding the Appelbaum investigation and six others for restoring trust in the project. The complete list is here.