How safe to run desktop remote access?

Most of the time, yes. Remote Desktop is used very often, mainly by IT personnel that need remote access to other servers (and sometimes PCs). Otherwise, they would have to go inside the computer room each time they wanted to perform their tasks.

If you are thinking about turning on Remote Desktop access on your Windows PC, that is a little different. By turning it on, you are giving someone else the opportunity to access your PC remotely. Making sure you have a very good login/password scheme will help from people breaking in, but normally you do not want Remote Desktop turned on unless you know the people that would access it.