Although we should not try to impress other people, we should take their opinions into consideration, for we should not do anything that can arouse unwarranted accusations of wrongdoing.
Accusing an innocent person of wrongdoing is wrong itself, and it is wrong for us to cause other people to do wrong, even if we cause it very indirectly. Secondly, if observers who do not know all the circumstances surrounding our behavior see a respectable person doing something which they had believed to be wrong, they may use this incident as an example for themselves that it is indeed right.
The Talmud states that the proper way to live is that which is honorable in one's own mind and will also appear honorable to others (Ethics of the Fathers 2:1). Attitudes are contagious, and how we behave does influence others.
This principle applies especially in the case of children. We all know the saying, "Most kids hear what you say, some kids do what you say, but all kids do what you do."
Although we cannot use what other people think as the sole criterion for our behavior, we must nevertheless consider that while God may know what is in our heart, other people do not, and we should therefore not cause others to come to erroneous conclusions.