In general, I thought IP addresses are mutable while MACs stay the same, and I thought that's why the outside world uses IPs to identify networks while routers inside a network use MACs to identify specific devices. If you can change your MAC arbitrarily, doesn't that risk making the router's job more difficult? Why not just assign yourself a different internal IP?
Changing your MAC will make older messages undeliverable, but that just means the connection will be momentarily interrupted until you establish new connections after re-connecting to the WiFi.
Why not just assign yourself a different internal IP? Because a. the router probably wants to assign you one itself via DHCP; and b. the router isn't looking at your IP address to lock you out; it's looking at your MAC address.
If your IP address is where in cyberspace you are, a MAC address is who you are. If you want to fool the bouncer, change your name, not your address.
The router recognizes a device based on its MAC and assigns an IP address. Traditionally, the MAC stays the same, so you’re right. In this case, OP doesn’t want to be recognized by the (airport) router. There is software for spoofing the MAC address for most platforms. Changing the MAC address has recently become more popular due to privacy concerns and on some operating systems it’s supported out of the box.