Flightgear: ILS makes my aircraft - Cessna 337 - turn away from the airport

In FlightGear, all manual ILS approaches work like a charm.

But many ILS approaches on autopilot are bonkers.

Steps to reproduce:

1. Approach Basel-Mulhouse (LFSB) from Mulhouse-Habsheim airport (LFGB).
2. Hit F12 for the radio/comms menu and select the ILS frequency for the RWY 15 approach, 111.55 MHz.
3. Hit F11 for the autopilot menu, and push in the dial ("Pulled Out" is unselected), and select NAV and ALT.
4. Depart and fly a course of 150 degrees magnetic. Line up with the ILS, intercept the glide slope, and select AP ON in the autopilot menu.
5. The aircraft turns away north-east.

One ILS approach that works:

1. Depart from LSPD, and fly due east. Align with the RWY 33 ILS of Basel-Mulhouse. The frequency is 109.35.
2. In the autopilot menu, repeat the same steps.
3. The autopilot flies the plane to the runway.

This is very annoying, as I don't know which ILS approach will work and which one won't.