How do you handle heated interactions with strangers in public?

I've had two such encounters in the past few weeks. In the first a woman followed me through the grocery store trying to hit me with her cart, then proceeded to rant and curse about how I wouldn't get out of her way. The second involved a woman at an outdoor market overhearing me make a height joke to my friend, then saying she would smack her husband if he said something similar and insisting the same should happen to me.

In the first situation I initially attempted to engage the woman to find out what was wrong. Rational discourse is healthy, right? Unfortunately she was more interested in threatening me than sharing information. I eventually realized that ignoring her was the least damaging thing I could do. Buy my groceries and leave, nothing I could say or do would appease her.

In the second situation I responded by carefully treating the stranger's statements as half-jokes. I didn't escalate, I didn't provoke, I didn't agree, I simply made innocent remarks until the line we were waiting in carried her away. I have no doubt she would have reached out and attacked me if I didn't tread lightly.

Each of these encounters left me a little frazzled, a little thoughtful. It's unfulfilling to just shrug these people off. There is a very real sensation of knowing they're in the wrong, I'm in the right, and I _need_ to communicate that to them, then everything will be just fine.

That goal sounds virtuous in a certain light, but I don't think it's a goal worth striving for. Isn't this sentiment that starts religious crusades and fuels online flame wars? Does communicating rightness in one-off social situations even matter?

I think the best way to proceed is to act neutral. Ignore the irrational stranger, though not pointedly, and leave the area, though not purposefully. Nothing is going to be gained by any directed action, and by cutting the interaction off quickly less is lost, too. Even if later I realize I was in the wrong, displays of rightness in the heat of the moment isn't productive.