Impolitic rhymes with:
broomstick, candlestick, capstick, chopstick, dipstick, joystick, krutick, lipstick, lunatic, nightstick, pitstick, politic, slapstick, uptick, yardstick
broomstick, candlestick, capstick, chopstick, dipstick, joystick, krutick, lipstick, lunatic, nightstick, pitstick, politic, slapstick, uptick, yardstick