1 to 1 NAT isn't doing any firewalling. Source NAT isn't doing any firewalling. Static NAT isn't doing any firewalling. All of these will generally just send traffic along if there's no other firewall rule associated.

When most people say "NAT", in the home user / consumer sense, they really mean "PAT": ports mapping to multiple private IPs using a single public IP.

"PAT" is not doing any firewalling either.

(It does rely on state tracking, which it shares in common with stateful firewalls, but you could run a LAN with either a stateless firewall or no firewall if you really wanted to meet the "nothing in common with a firewall" requirement.)