I found an interesting audio recording of Fr. Hesse, where he describes Opus Dei as "the heart and the brain of the conciliar church." Other forum members have probably already heard this at one time or another.
Fr. Hesse also says that Escriva admitted Communists as members of Opus Dei, even though it was an excommunicable offense to be a member of the Communist party at that time. He says too that the founder of Opus Dei (Escriva) wanted a Church based on the laity, which makes sense. It's possible, IMO, that Opus Dei and it's friends and supporters don't want a group that has a strong priesthood to gain any momentum, such as the SSPX (which is not really so strong anymore, IMO, but they don't realize that).
Fr. Hesse audio: