How to avoid collisions with already printed objects?
The problem was twofold:


Lack of bed adhesion due to the small contact surface
motion into the already printed objects.


The quick and dirty way was to change two settings:


Print with a small (3 mm) brim to stick the supports to the print and provide more surface. Other materials than PLA may need considerably more brim!
Activate Z-Hop to force the nozzle to lift over the print when traveling


These tricks don't solve issues with very thin structures or in all cases. In those cases, it can be mandatory to increase the structure's (support) thickness or change the alignment.