Why, exactly, did the Austrian and German federal governments open their borders on September 4? Die Welt has an interesting, though thinly-sourced theory (g) about the immediate trigger. Austrian pro-migrant activists had already started to drive in their private cars across the Hungarian border, pick up migrants, and drop them in Austria. The problem is, under Hungarian law, this constitutes human smuggling. Therefore, Hungarian border police would be required to arrest Austrian activists bringing people across.
The activists had decided on a concerted drive-across action on September 6. This brought all sides into panic mode: Would Hungary really be forced to arrest hundreds of citizens from a fellow EU state who were, in the words of sympathetic officials, 'just trying to help'? This prospect was so unappetizing that Austrian Chancellor Werner Faymann decided to avert the potential diplomatic crisis by simply opening the borders. Not wanting a massive backlog of migrants stranded in his country, he called Angela Merkel and they both agreed to open the borders.
This story cites no named or even unnamed sources, so it should be taken with a huge grain of salt. Also, I am sure the activists weren't the sole reason for the decision, even if they were the immediate reason for it. But if it holds up, there are small number of Austrian left-wing activists who can take the credit for changing the demographics of Germany for decades. I'm sure they're quite happy about that.