In some cases yes. I was thinking more along the lines of people who get asthma attacks or have anxiety issues and other conditions that can be triggered by a face mask. For people with more permanent conditions that can be made worse by wearing a mask it makes sense for them to avoid potential exposure as much as possible.
People who are around them in close contact should take care to practice common sense sanitation, keep from directly breathing on them and yes wear a mask. (A clean dry mask which has been properly washed and dried and fits properly) This is to keep down the possibility of respiratory infection spread by larger droplets. Just as they should during flu season.