Therefore being part of the problem is a problem for God.
Yes! I believe that "her sins have massed together clear up to heaven and God has called her acts of injustice to mind" (New World Translation) means the effect of her sin falls also on the innocent. It is a problem.
266 hamartía (a feminine noun derived from 1 /A "not" and 3313 /méros , "a part, share of") – properly, no-share ("no part of");
http://biblos.com/revelation/18-5.htm
I am sure this scripture and the one that says "no flesh would be saved" is descriptive of the same problem.
It's not required to be part of the solution,
Maybe so. But this rule does not apply to all.
The justice belongs to God but the execution of justice belongs to us. Everyone of us. It is obvious that so far that isn't happening.