I was able to answer my own question. The screw threads should not engage the plastic. When removing the screw, the hole was noticeably more loose, so I used the threads of the screw as a file and cleaned up the hole. After this, the screw slid through cleanly.
Is the M3x25 screw supposed to thread into the plastic part, or should the screw slide through? I suspect the holes might be too tight on my idler housing and the screw is warping the sides inward as it is tightened.