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You can call the things mangling IP addresses and TCP/UDP ports what you want, but that will unfortunately not make them go away and stop throwing away non-TCP/UDP traffic.

And by your definition my home router is not a router since it does NAT? There's really no point in arguing semantics like this.

We're discussing nonstandard IP protocols. In that context, your home router is a CPE, and not described by the term "router" without further qualifiers, because that's the level the discussion is at. I'm happy to call it a router when talking to the neighbors, when I'm not discussing IP protocols with them.

Both things come on the same box nowadays.

There are many routers that don't care at all about what's going through them. But there aren't any firewalls that don't route anymore (not even at the endpoints).