There’re some really bad people who harass journalists. Women and minorities, especially, are the targets of extreme vitriol. Yet many newsrooms do little or nothing to attempt to protect their employees, or to think through how journalists and organizations should respond when harassment occurs.
Harassers and trolls have multiple motivations, often simple racism or misogyny, or in support of misinformation, or to suppress law enforcement or intelligence operations. Frequently, what appears to be multiple harassers are actually sock puppets, Twitter bots, or multiple accounts operated by single individuals.
Sustained harassment can do some serious psychological damage, and I speak from personal experience. Outright intimidation is a related problem, suppressing the delivery of trustworthy news—the kind of news reporting that is vital to democratic governance.
The usual solution is to ignore trolls and harassers, but they can be persistent, and they often game the system successfully. You can mute or block a harasser on Twitter or Facebook, but it's easy enough for them to create a new account in most systems.
If you're knowledgeable in Internet forensics, you can sometimes trace a harasser’s account, and “dox” them—that is, post personally identifiable information as a deterrent. However, that really needs to be done in a manner consistent with site terms and conditions, maybe working with their trust and safety team. (Seriously, this is a major ethical and legal issue.)