Maybe we could request a tutor to educate us on the culture in the village? It's not as quick as immersing ourselves in the culture by freely mingling, but hopefully it won't cause any more social faux pas. Ideally, we could get two or more tutors by playing Yoshida, Gasai, and Takahashi off against each other to ensure that our education hasn't been purposely altered in some way to serve any of their own ends. Hell, the more people we can convince to come by our base and socialize the better.
Personally, I want to turn this village into a staunch base of support and later on have its members be our fully fledged allies. To do so, we will have to learn their customs and show them the respect we would give to any of our teammates. The more we put off learning about them for the sake of our own team the more the xenophobic isolationists will sway public opinion of us that we are only interested in looking our for ourselves.
If we want to befriend the village, we actually have to try to be their friends. Friends learn which subjects in simple conversation are tolerated and which topics cause distress. We aren't antagonizing Keiko by demanding what her relationship with her biological sister is like, so why are we, through our inaction, causing similar distress to the village members?
We can still assuage our teammates feelings after the recent near-miss, but we should also try to reconcile with the villagers. A simple "Sorry we sorta kinda traumatized your kids with that training accident, if you don't mind, could you tell us how you train? We would rather not make the same mistakes as last time," would be a less than idea starting point, but we have to start somewhere. Once we have a dialogue with the normal people in the village (which I hope would not be considered meddling in politics) we can start repairing our public image and/or adding to our knowledge of how the village functions at the lowest government levels.