Opus Dei has been accused of this for a long time, often because they don’t publish a list of members, or because their centers and corporate apostolates don’t have religious-sounding names, or some such reason.
In my opinion this is due to a misunderstanding on the part of some of those in the Work and those outside the Work about what the general public has a right to know. For example, it would not be proper for Opus Dei to publish a list of members. Membership in Opus Dei is a private matter. However, the public does have a right to know of a foundation or corporate work’s affiliation with Opus Dei.
Another explanation for the secrecy, real or perceived, is that given the attacks Opus Dei has suffered over the years, there is sometimes a reluctance to open themselves up to situations where their words or actions can be misconstrued.
Another frequent criticism of the Work is that prospective members (especially numeraries) are sometimes advised not to tell their families for some time that they’ve joined the Work or are considering doing so. When I joined Opus Dei I was given this instruction myself and it is sometimes still given.
Frankly, I don’t know why it’s given, and it seems kind of odd to me. Still, to put this in its proper context I think it might be helpful to remember that during its early development in Spain the Work was viciously attacked by people who truly didn’t understand what it was that St. Josemaría was trying to do. Opus Dei was an entirely new reality in the Church, and there was nothing for parents to compare the Work to so they could get a better understanding.
Nevertheless, parents have a very important role to play in a young person’s discernment of his vocation. They know the person better and love him more than anyone else. I sincerely believe St. Josemaría would be the first to agree with this. But he would also say that parents should educate themselves about Opus Dei if their son or daughter is considering a vocation before giving their advice. And parents should realize that it is their son or daughter’s decision, just as much as it would be if they were considering becoming a priest or nun.
In at least some cities, if a young person is considering a vocation to the Work, the director of the center will meet with the parents to answer any questions they have, and if the parents don’t approve, the person is not allowed to join until he is older.
It’s my hope that as Opus Dei becomes better known, all the circumstances that might lead to a young person being given this advice will become less and less frequent.