LAN is being used in an under specified way. To my reading, a separate VLAN or standalone LAN for the washing machine wouldn’t be on “my (main/primary LAN is assumed here) local network” if I mean that “my local network” doesn’t have untrusted devices on it. I tend to read these kinds of comments with a bit of wiggle room because sometimes folks disagree about if VLANs are actually isolated enough to consider them separate local networks, as the same device may do routing and firewall or VLAN tagging, so there is isolation in principle, but bad actors can’t be expected to comply with network security policies.

I guess I can see how each of you could be right to their own reading.

This is my setup. I find this to be a reasonable balance for comfortable life. Except my printer, that gets no Internet so it cannot update to some crappy firmware that nags about supplies.