Why does my toilet make a loud rumbling noise when flushed?
Turns out the loud noise was caused by water rushing from other fixtures.  The house had galvanized steel pipe as the main feed line (off the meter) which had become restricted, so when the toilet could not pull enough water from the main line it sucked it from other lines.

Replacing the galvanized pipe fixed the issue (as well as increased the pressure to the entire house).