Methinks they've run across evidence speaking against the divinity of Jesus. That alone would ruin any number of agendas if it leaked out.
There's nothing of the New Testament among the DSS. A Spanish Jesuit, José O'Callaghan, has argued that one fragment (7Q5) of 14 characters is a New Testament text from the Gospel of Mark 6:52, but his interpretation of the characters is disputed. It might be just a unknown commentary just like the rest of the scrolls found in the same cave (#7)
Anyhow, to be a copy of Mark, the ink would hardly be dry to be included with the rest of the OT scrolls buried at the time (~ 30-60AD). Then there's the question of why the Essenes, a group of Jewish extremists, would have anything to do with the liberal Christians that seemed to flaunt the law of Moses?