There are times when it makes sense to operate a "closed" small group—a group that does not seek to bring in visitors or add new members. But the following common reasons for closing a group are not among those times.
Our Group Values Closeness
Developing close relationships should be a high value of small groups. Your group is where everybody knows you, unlike the sea of thousands on Sunday morning. But there is a line where closeness causes a group to become in-grown. The motto changes to "Us four and no more" or "We seven going to Heaven."
The problem is that what was once so great for your group—closeness and intimacy—will likely become the death of your group. Over time, members will move away. Schedules will conflict. As your group begins to decline somewhere around the two year mark, you will find it hard to recruit and keep new members. There's too much history going on. When it's all said and done, your group will be done.
Open groups enjoy meeting a steady stream of new prospects. Some will stay. Some will not. And that's okay. The core of the group will continue to become close. The new members will start out as the "ministry" of the group, and over time they will become close-knit as well.
Outsiders Might Upset Our Rhythm
People become comfortable with familiar patterns. They sit in the same place. They make the same inside jokes. They even greet you the same way every time. (Pay attention and see what I mean). It doesn't take long for a comfort zone to become a rut. Then, when prospective members visit your group, everything is upset. The new folks don't understand the jokes. They don't know the routine. They might even sit in your spot!
Your group won't be the best fit for every prospective member. Every group has a personality. It might be a good idea to "interview" the prospect who is looking for a group or meet with them days before the group meeting. You will get a good sense of whether or not your group will suit them.
I know that if people visit my group expecting me to be "the pastor," they will probably be disappointed. Our group has a weekly Bible study, but we're not parsing Greek verbs and digging through commentaries. Our group is led by "Allen, the guy who is a pastor." It's not for everyone. When someone asks about our group and I don't think it would work, I tell them: "You probably wouldn't like my group. But, here's a group you would really like." But there are people who ask about the group who fit in very well. I do my best to figure that out ahead of time.
Confidentiality should always be a very high value in a small group. Groups are defeated and often destroyed by loose lips. Anything said in the group should stay in the group, even if you know the other parties involved.
But it is certainly possible to value confidentiality and still include new members. When a new member joins the group, simply go back and review the Ground Rules, Group Agreement, or whatever you call it. The conversation could go something like this: "Since several new folks have just joined our group, I'd like to take a few minutes and review our group's Ground Rules. One of the things we value strongly in this group is confidentiality. Anything that is said in this group needs to stay here. Agreed?" If they agree, then you're good to go. If they don't agree, then they're out the door. I doubt that you will need to kick anyone out.