They could however sue individuals or organizations.
Via The Hill:
A federal judge ruled Thursday that a Louisiana police officer could not sue Black Lives Matter after he was injured during a protest, saying the social movement could not be blamed for his injuries.
” ‘Black Lives Matter,’ as a social movement, cannot be sued, however, in a similar way that a person cannot plausibly sue other social movements such as the Civil Rights movement, the LGBT rights movement or the Tea Party movement,” Chief Judge Brian Jackson said in a ruling, according to Reuters.
Jackson went on to write that an “associate entity” could be held liable, however the judge said the unidentified officer did not provide a sufficient case against the group and the individual.