No. A public IP address is not required for KeepYourHomeIP VPN.
KeepYourHomeIP is designed to work with any type of IP address. Whether you have a dynamic, static, public, or Carrier-Grade NAT (CGNAT) IP address, KeepYourHomeIP is compatible and ready to go.
It also works with any Internet Service Provider (ISP), including Starlink, and supports cellular connections.