Normally each party gets to appoint their own committee members. Whether McConnell has any special power to decided to exclude opposing party members from a committee, I don’t know, but he sure could raise hell with Schumer in various ways if Schumer does not cooperate. Whether the Turtle will really put the screws to Schumer over this, who knows?
McConnell should first put the screws to Republican chairman Burr and throw his tail off the committee. The man has been a disaster.