No person who has been convicted of child abuse pursuant to chapter 26-10 ; a sex offense pursuant to chapter 22-22 ; or, within the preceding five years, any other felony; and no person whose name appears on the sex offender registry or on the central registry for child abuse and neglect may: (1) Be licensed to operate a child welfare agency pursuant to § 26-6-14 ; (2) Be registered to operate a family day care home pursuant to §