What kind of public schools display crosses in the first place?
Austrian and Bavarian ones.
That's very unfortunate. Do they evangelize as well?
No.
However, the Catholic and Lutheran churches oversee separate religious education, within the government school system, for their members. In some areas/years, they keep everybody else entertained with a nondenominational "ethics" class. Elsewhere/at other times, they just put Religion at the start or the end of the day and provide kids with a great incentive to want to leave the church.
Yes it's weird.
But it's the way it is. And talk and half-assed negotiations to provide some sort of Islamic religious education on a par with it have been going on for years and years and are going nowhere.