No, they should, for the exact reasons people dislike vocal christians.
This is from personal experience and from most of the middle of the road types I know. Religion is a personal thing, and everyone is free to make their own choice. We're not out to save people, or convert them, or even tell them how, who, or why to worship. That is the realm of extremists and jihadists.
Most moderates just want to do their thing, live their life, and worship how they choose.
I guess it's that message they should be vocal about; that religion is a personal thing, not to vocalize the teachings of Christianity.
But it is interesting because how then can you be an effective and good Christian and NOT spread the word. It is right in the book of teachings to do exactly that.