HankD, Capitol Hill Baptist Church does 'small groups' now, for an explanation, the website directs to the following article written by its then Associate Pastor. Bolded is the part relevant to the taboo expressed in the OP, leadership qualifications follow:
9Marks • Small Groups at Capitol Hill Baptist Church
"HOW ARE SMALL GROUPS STRUCTURED?
With the exception of groups based on gender or devoted to couples in their first two years of marriage, all our groups are open to anyone. We recognize the benefits single-sex groups can have in facilitating a healthy vulnerability and accountability, especially for the large number of singles in our church. And young married groups
led by older married couples can be used to help newlyweds put their marriage on good biblical ground. But
beyond that, we are hesitant to particularize much further, since we want our church members to understand—as we continually remind them!—that one of the gospel’s first implications in our lives is learning to love people who are not like us."
"Groups generally have a leader and co-leader....We expect the following of small group leaders
• They must be members in good standing;
• regularly attend both Sunday services....It’s hard to stay up on the life of our church without being at both, and we do not want to hold up people as leaders and models who are unable or unwilling to make this a priority;
• be prepared to study and prepare content coordinated and approved by a pastor;
• communicate regularly with the church office about pastoral issues;
• be willing to create an open culture, and accept new members;
• generally care for the group;
• facilitate discipling relationships;
• attend quarterly training events."