Brian Atkinson asks
What are appropriate ways to share your faith at work?
He suggests four ways: know your audience, know your Gospel, know how to love, and know who needs to repent.
I can think of another.
The missing biblical aspect is simply to know your job. We are known (and trusted) by how we live publicly, that is what gives warrant to our convictions and testimony. They know us first, trust us, then listen to us.
As to the Coppedge case, it appears that he had been outspoken in ways that created distance between himself and his colleagues (e.g. rename the holiday party a Christmas party, vocal in defense of Prop 8). It’s this aspect that others should follow, this aspect of advocating derivative Christian positions as it were, that creates the distance and has others not trusting, not wiling to listen. In a workplace, task focus is important. The workplace is a community, and in that community we witness differently than we do in other aspects of our lives.