I am guessing the resistors are included because the board was intended for use with 5V AVR but the vs1053 used 3.3V logic. Since Due uses 3.3V logic the resistors are not needed and must be removed. Is it possible the other pins such as _reset, _cs, _dcs have the same problem?
The Adafruit VS1053 feather wing board is designed for 3.3V operation. I used it with an ESP8266 board (3.3V logic) with no problems.