Vulnerability means removing one's mask as much as one is aware of. Letting one's hair down, as we say. Being real. Not putting on a front.
That all needs to be tempered with love. The love of God. The love of the Spirit. Love for one another. In other words I won't do that which would violate love for my neighbor or brother or sister. They may not be ready or able to handle my admission or confession. Though I think there is a needed point of contact when another knows we are as human and "cracked" as they are. We shouldn't go out of our way to do that. It will come natural and in time enough.
I heard someone say recently that there is no way they're going to open up in a group of believers in which new people are coming in. I can understand that. And besides, there needs to be in such groups an emphasis on confidentiality as well as commitment to prayer for each other.
But we need to model being vulnerable. It will help others open up, if we open up. Only in the context of community and friendship should we do so. But our real selves aren't penetrated by the Spirit until we expose our real selves. As we do that, others can empathetically enter in and the dynamic of the Spirit through their love and prayers can make a difference in our life.
I notice in Scripture that characters are voluntarily and involuntarily vulnerable. Over and over again. Including Jesus himself. So it seems we ought to not be averse in doing so. Maybe instead, this ought to be part of who we are and what we do. Before God. And wisely, before others.