Sincerity and Directness of Singing

If the singer sings sincerely and with directness of feeling, then that singer automatically gets my admiration. Some degree of acting is required, unfortunately, when singing a song one no longer emotionally connects with. How does one avoid coming off as emotionally flat in these circumstances? Or is it best to avoid material which feels emotionally distant altogether? I suppose established artists face this challenge when an audience is screaming for your hit, but you want to sing your new, more emotionally relevant material, yes?