Viruses had only been discovered a few decades before this picture was taken. It’s very likely that the family (and most of society) had no understanding that the virus was unlikely to jump species and so took the same precaution to keep the cat from spreading the disease that they themselves took. I’d rather people made this sort of mistake than the willful idiots we had this time around refusing to believe in viruses at all.

FYI the Spanish Flu’s origin was a pig farm in Kansas.