I don't have any problem with them calling it horrific, horrible, or whatever. People are entitled to their opinions, and have the right to state them. Although Twitter also has the right to delete them.
But anyway, what I'm taking issue with is the argument that archaeologists et alia don't have the right to be nonjudgmental. Also that being nonjudgmental isn't the norm for archaeology as a profession.
I don't expect your average Twitter user to know that. But at least, they should understand the concept, if explained well enough. After all, it's also the norm for physicians, attorneys, and psychologists. Even judges, who are supposed to interpret law objectively.