They can - but it's unlikely that most of the images hosted on FR would contain a virus.
One potential problem area could be in FR's Caption This Image section, where anyone could upload an infected image. But I think John R. has coded some restrictions in that feature to prevent embedding of those images in other web pages.
Most images seen on FR are actually hosted on a different server, which may or may not be running Linux.
That's what I thought - which is why your original statement - "FreeRepublic is already doing it's part to improve security by running on a Linux server. " - adds nothing to the thread but might conversely give users a false sense of security.