<nitpick>If it is plastic, it is not really old. I have plumbing that pre-dates Unified threads. It is probably Sellers thread, but since it is hand-cut it is very hard to tell. Try getting anything you buy today to fit on that. I finally wound up using gooseneck Teledyne shower heads and cutting new internal threads on the end of the gooseneck.</nitpick>
Plumbers and health people needn’t tell me of the dangers of old lead and cast iron pipes - everything involved with drinking water (and a lot more) has been replaced with modern copper. I’m not about to rip into walls of irreplaceable 1920’s “subway” tile to change the shower and toilet pipes if I don’t absolutely have to.