If they had religious objections to the police, and thus refused to use them, would we start seeing stories that they are being robbed and the robbers are getting away?
If they had religious objections to invoking the police, it would be irrelevant. The police are still going to track down the robbers and arrest them regardless of whether mom and pop want to file charges. In structuring our society, we have arbitrarily decided to make a legal distinction between certain types of injustice. It used to be the case where I live that domestic violence was not prosecuted unless the abused wanted to press charges. You'd think if someone was being abused they would want their abuser to get what was coming to them. But that is not always the case, I suppose we decided we wanted the abuser to face justice regardless, because now they will be prosecuted by default.
It is just as arbitrary deciding we are going to rely on a civil enforcement of contract law. In fact, we do have measures to protect certain disadvantaged people in contracts---minors, people with mental defects---but so far not people averse to filing lawsuits. Just because the Amish are willing to allow injustice to be perpetrated against them doesn't make it okay and doesn't mean we as a society are obliged to accept it, any more than we are obliged to allow physical abuse simply because the abused wants to remain in the relationship.
The reason the Amish don't wish to file a lawsuit is because they have a different set of priorities. Their goal is to make their lives a compelling argument for what they believe in. They are instructed to shun lawsuits because legal disputes often result in discord and when it comes to a choice between the money or maintaining goodwill they suppose money is not that important. You're right that it is their choice to make. But it doesn't change the fact that they are being wronged and cheated. I don't understand why you think they need to be actively trying to get the better of their oppressors before we're allowed to be sympathetic.