Paul and Silas were dragged into the  market place before the magistrates. In ancient cities the law courts was not a building it was a place in the middle of the market. It was called the bema seat on which the judge sat. People would bring to him their squabbles with other people. The only way they could win was to shame him and make the person look as bad as possible.  Character assassination was necessary, so they dreamed up as much negative evidence as possible. Anything they could say in order to convince the judge.  It often was very entertaining for the market crowds and people would stop on their way home from shopping for a look at the slanging match.  Paul is saying that sort of match between two Christians who can no agree, will hinder the gospel as they will be in a position where they have to slander and shame the other brothers or sisters.Friends, then as now we are to be conscious of the witness our life is to others who are watching!