Politics of a United, Neutral Germany post-1945?

The idea of a prospective Neutral Germany has been discussed on this site quite a bit over the years, primarily what if the Molotov note in 1947 or the Stalin note in 1952 had been accepted by the west - regarding whether these proposals for a unified Germany were sincere or not is a matter of debate in itself. Otherwise had Beria or Malenkov emerged as Soviet leader post 1953, as both were in favour of proposals for a unified, neutral Germany. A Unified, Neutral Germany would have profound effects on the Cold War, and US-Soviet relations postwar.

What hasn't been discussed as much is the impact of a non-divided Germany on Germany itself, particularly in the political sphere. One of the reasons the CDU achieved such political dominance post 1949 was that many of the strongest areas of pre-1933 SPD support were now under Soviet occupation, and had Germany remained unified and democratic the SPD would surely have emerged as the largest political party in the inaugural post war elections.
The SPD in the eastern bloc succumbed so soviet pressure in 1946 and merged with the KPD to create the Socialist Unity Party, which was in effect the KPD under a different name, so lets assume a POD earlier than this.

Assuming an accomodation is made almost identical to that of Austria in 1955, where Germany becomes a liberal democracy outside NATO membership. What would the domestic politics of a unified Germany be like in the 1950s-1990s? Would the SPD, like the scandanavian social democratic parties, remain the largest and dominant party?
Okay - I'll have a try at this.

Germany isn't one homogenous entity but made up of the different provinces (Or Lander) each of which has its own characteristics.

You have the rural socially conservative areas like Bavaria, Prussia and Schleswig-Holstein and the more industrial areas like the Ruhr and Silesia.

It's often forgotten the West German SPD was essentially Marxist until the adoption of the Godesberg programme in 1959 which led to its evolution as a broad centre-left party and paved the way for Brandt to become Chancellor in 1969.

On the left, we would have both an SPD and a KPD and I suspect the former would move more quickly to the post-Marxist positions of Godesberg so perhaps in 1955.

The CDU would be able to become politically active in the former Russian controlled areas for the first time since 1946. Would a Catholic-dominated centre-right party achieve the same level of support in the Protestant east or would it also face competition from a socially conservative grouping or would such a grouping join the "Union" of three broadly centre-right parties.

Would the German Party perhaps do better in the former Russian areas and be the third part of the centre-right "union".

So you'd have the CDU, CSU and DP against the SPD and KPD with the FDP sitting between the two blocs.

Does neutrality extend to economics as well as defence? Presumably, there's no ECSC or the new German state leaves it in 1953 and therefore no EEC or EU as we know it. Would part of the agreement forming the new neutral Germany mean no foreign troops on its soil? Presumably but that wouldn't stop Russian troops being in Poland - in response, would we see American troops in Belgium, Holland, Denmark and France to also guarantee German neutrality?