#blackouttuesday is a good idea in theory, but could prove detrimental to those attending the protests, who are the most in danger.
Social media has been the most effective weapon of the Black Lives Matter. Encouraging everyone not to post takes away their primary means of sharing information about what is happening at the protests and has been proven to be one of the few ways to hold participants on both sides accountable for their actions.
By not posting anything, you leave social media streams wide open for those looking to undermine the protests to flood the various platforms with misinformation.
Please, by all means, continue to show your support by posting a black square and/or blackout your profile photo. However, the best way to support Black Lives Matter is not to go dark on social media, but to continue to share information that helps further the cause.