Maybe, but I don't think they are in the sense that really matters. First, I think a lot of people just see social inequality as a global problem, like all the refugees coming there from poorer countries.
Second, the impression that I often get from Germans is that they are all for helping people in dire straits but at the same time thinking that they are somehow excluded from ever getting into such a situation and that for people that do it's their own fault and they are somehow worth less for it.
[1] https://www.ipsos.com/sites/default/files/2017-08/what-worri...
However if you show people what social inequality actually looks like in their own country they will dismiss it because that's not social inequality, that's just talking about 'Assis' (i.e. the people in dire straits who are themselves to blame for their situation, as I mentioned in my previous comment).
It did help to break Merkel's popularity when Martin Schulz was first elected as a candidate of the SPD and a lot of people thought social inequality and social justice would be a big topic of the election. The SPD lost all that support again when it turned out their strategy for making social inequality a topic in the election was just saying the words "social justice" a lot with no substance to follow up with.
It appears to me that Germans are very aware of social inequality. Minimum wages and restrictions around contract work were attempts to slow down the trend of growing social inequality. It hasn't stopped it but I think no country has yet found a way to stop/reverse the inequality brought by technology.