Membership of a private club or society is, by intention, a private thing. It is a matter between a person and the institution, and the institution is generally discreet about its members. Yet membership is rarely as unrecorded as it feels.
A club is private, but it is not invisible. It has premises, and members are seen at them. It has a history, office-holders, events and committees, and these generate records and mentions. Members appear in connection with it, are listed in its materials, or are noted as having proposed or seconded others. Over time, an affiliation that was never announced becomes, for anyone who looks carefully, reasonably easy to establish.
What membership reveals is not trivial. To belong to a particular institution is to be placed within a particular milieu: a set of values, a level of standing, a network of others who belong to the same place. Memberships, taken together, sketch the shape of a person's world, the circles they move in, and the people they are likely to know. For someone assembling a picture, affiliations of this kind are valuable precisely because they connect a person to others.
There is also a chain of association. The other members of a club are connected to a person by that shared membership, and each of them has their own visibility. A discreet individual in a well-documented circle is described, in part, by that circle.
None of this is a reason to belong to less, or to treat one's affiliations with suspicion. Belonging is one of the quiet pleasures of a well-lived life.
It is a reason to recognise that affiliations are a form of information, that they tend to become known, and that an honest account of what is visible about a person includes the circles they are understood to move in.