The Mishna in 3:2 says The one donating the shekalim should not come in to the shekalim chamber in various modes of dress such as with shoes or with teffilin or wearing a long cloak. The Mishna explains the reason so that people should not suspect the he possibly stole money from the chamber and hid it in his cloak or these other items. What is wrong with that? The Mishan explains that if he should possibly at some point become poor they will say that it is a punishment for having stolen the money from the chamber. if he became rich they will say it is because he stole that money. The Mishna then proves from some pesukim that one must always be conscious of his good reputation amongst people, just as he is careful about his actions in relation to Hashem.
It is not enough to do the right thing. One must also do it the right way.
This does not mean that one should cater to everyone's preferences. Just because some people feel something should be done one way over another, etc. you do not have to do what they want. What I am saying as an explanation of the Mishna is that you should be careful to do the right thing (as you understand it or with the psak and advice of your Rabbonim) and you should be careful to do it with honesty and integrity in a way that nobody can suspect you of having done something wrong.