A Stoic always does what ought to be done (i.e. what is virtuous). To him or her, it does not matter what others think. It if is right, the Stoic does it. If it is wrong, the Stoic does not do it. Epictetus summarizes this attitude as follows.
When you decide that something must be done, then do it without ever being shy that you’re seen doing it, even if many people will think differently about it. Because if you’re doing something that’s not right, avoid doing it; but if it is right, why would you be anxious of those that reproach you wrongly.
There should be no shame in doing the right thing. Some Stoics actively train to abolish shame. Zeno, the founder of Stoicism, was taught this by his teacher Crates. Crates one day gave him a bowl of lentil soup – which was considered the food of poor men – and instructed Zeno to walk through the city with it. When Crates saw that Zeno was ashamed and tried to hide the bowl, he broke it with a blow of his staff, leaving Zeno drenched in the soup. Apparently, Zeno ran away with Crates shouting after him: “Why run away? Nothing terrible has befallen you!”. A harsh lesson indeed, but a valuable one.