To put it plainly: Köhler is a hack. And politically not neutral. Anyone who argues about that makes themselves look ridiculous. Very few German federal presidents were truly politically neutral - and hacks were certainly more than just Köhler and Carstens. However, it is undeniable that Köhler's election and term of office are hard to surpass in terms of embarrassment - but this is by no means due to Köhler alone.
I also still remember well the praise that came for him even from the SPD camp when he was proposed and then elected. I thought it was pitiful of the Union to ram through such an emergency candidate (after they had almost torn themselves apart in strained attempts to come up with a presentable candidate) just because they once again wanted to play out their majority - purely on principle, even though it made no sense. But pitifulness is what characterizes federal politics at the moment - both in the coalition and in the opposition.
In that sense, a hack as federal president is also fitting ...