We don't normally worry about security in ham radio, because we can't encrypt our transmissions anyway in the vast majority of cases. Some niche protocols support authentication of messages, but that's it, unless you're controlling satellites. There is nothing except regulations and etiquette stopping me from making contacts using any mode with someone else's call sign, and if I use a digital mode, there's no way for anyone except me and the person I'm impersonating to tell. It is certainly possible for me to eavesdrop on other people's conversations, and this is neither illegal nor unethical.
However, when we use digital modes, our computers are processing arbitrary data from an untrusted source. Since security isn't really a concern for most hams, it's unlikely that ham radio programs such as fldigi and WSJT-X are tested for responses to invalid data; it's quite possible that some ham programs have remote code execution vulnerabilities or similar bugs. There is nothing (again, except regulations and etiquette) stopping a hacker from making transmissions intended to exploit such bugs.
I found a few articles about people hacking their own computers over ham radio for experiments, but have there been any documented cases of a ham radio operators' (or shortwave listener's) computer being compromised over an amateur radio digital mode without the owner's permission?