Historically, from my experience, personal questions like that have traditionally been avoided. It can lead to biases and prejudices against that individual. More importantly it seems clear to me that religious affiliations lead to intolerance, bigotry, dualism (my religion vs.your religion). So religious affiliation on FB would lead to separateness when I think the goal is "that we are one in the body of Christ?!"
Yes, I believe that is the wise response. Proclaiming our religion to others, that may not understand, can prejudice them. In the boxing ring it would be called leading with the chin. When our goal is to be helpful to others, prudence is a virtue that carries a high rating. Why screw up a future chance to be helpful; by branding ourselves religious fanatics or religious bores. It is NOT the world that I am trying to reach; it is you, sitting next to me.