Come to think of it, I wonder whether it is the electronic thermometer that resulted in most young adults not remembering rectal thermometers. Let me explain.
1) For infants and young children, it was later possible to take temperatures in the ear or other method. Back then it was only rectal.
2) Even though rectal is still much used nowadays for infants and small children, an electronic thermometer takes seconds to register. This does not compare to being face down with a thermometer in the rear, perhaps held on mommy's lap, for minutes with the thermometer in. There are higher chances that the child would remember a longer (and more embarrassing) rectal temperature.
3) It is possible to take oral temperatures at a younger age with an electronic thermometer. With a glass thermometer, this entailed having the kid with the mouth closed, thermometer under the tongue etc. for minutes, which is hard for small children; compare with doing it for only ten seconds with electronic.
4) With mercury thermometers, dropping the thermometer to the floor and breaking it (or whatever other reason to break it) meant a complicated cleanup of a dangerous chemical. Caregivers were thus more likely to take precautions (holding the thermometer in...), whereas oral with an electronic thermometer may be done while standing, at no risk.
But perhaps there are also changing attitudes towards privacy (when I grew up, a child was entailed little privacy with respect to adult caregivers).