How to be connected to two different LANs simultaneously?
Martin,

You have set up two conflicting networks in the Mac.

The way to fix this is to tell the Mac exactly what you want to do which is, I assume, to share your Mac's WiFi 'net connection over Ethernet to your Linux box.

The first thing you need to do is take out all references to a network over the Ethernet interface as Sharing will take care of all that. So if you have manually set IP addresses and such then take all that out.

Open System Preferences > Sharing and select Internet Sharing. Then in the drop down "Share your connection from: " choose "Wi-Fi" and in the box tick "Ethernet".

This should fix your problem but it might require rebooting the Linux box.