Another way is "When we don't have strong support from our political system, we must stand up and fight for justice ourselves". I think you do not need ourselves but that is up to personal choice.

You can't really say "a backup" like that. Instead you can say "When our backup isn't strong"

I understand about having to not be direct about government, so you can make reference by talking about other types of leaders, like this: When we don't have strong support from those we trust and expect it from such as schools, teachers, leaders and the like, then we must stand up and fight for justice. "and the like" in this sense means "related" or "similar to" or "and so on". Good luck!