I just tried it for fun … yes you are correct …
the latitude should not cause the AP not to follow the ILS localizer. … (the GS is captured correctly. Nevermind me being a bit high due to the strong tailwind but I wanted to test RWY35 as you did).
First I thought maybe it is an offset approach, but it isnt. Secondly I thought, maybe one of the many MSFS database bugs of not having the ILS localizer aligned correctly with the runway, but that is correct as well (see LNM and using MSFS database).
So most likely one of the many bugs of the MSFS Flightplanner / AP (although I use the WT G3000 7.4a, the underlying Flightplanner/AP is still MSFS at this point).