Does Route by Zaweba work on Mac or Linux?
Yes. Route by Zaweba has a Mac and Linux version that uses the same routing engines, map regions and .ozroute files as the Windows app.

It does. Route by Zaweba has a Mac and Linux version that uses the same engines, the same map regions and the same .ozroute files as the Windows app. A round planned on one system opens on another, and the way the app works is the same on each.
That consistency is the important part. A route planner is only useful if the plans you make can move with you, and sharing one file format and one set of engines means they do.
What carries across
An .ozroute file is a JSON file holding your stops, time windows, options, set-off time and via points. Because the Mac and Linux version reads and writes the same files, a weekly round saved on a Windows PC in the office can be opened on a Mac at home, or on a Linux laptop in the van, without converting anything.
Map regions follow the same pattern. A region is prepared from an OpenStreetMap extract into an address index, a routing graph and map tiles, and the Mac and Linux version uses the same regions. The routing engine is the same too, so the same stops and options give the same routes.
What Route does, whichever system you use
Choose a region from Geofabrik's list of continents, countries and counties, or prepare an .osm.pbf file you already have, and the map, routing and address search then run offline. Search as you type for towns, streets, house numbers, named places, full or partial UK postcodes and coordinates.
Plan from A to B, fastest or shortest, avoiding motorways, tolls or ferries in any mix, and drag the line to add via points. Build a round from search, right-clicks, a CSV file or a GPX file, give stops a time at stop and a time window, and use Optimise order to put them in the best sequence with a fixed start, a fixed end or a return home.
Every leg has turn-by-turn directions with distances and times, a set-off time gives arrival and departure times for each stop, and with your mpg and fuel price you get the fuel cost. Then take it with you as a PDF route sheet, GPX for a satnav, Google Maps links for the phone or stops as CSV.
Why a planner on more than one system helps
Teams are rarely all on one kind of computer. An office might plan rounds on Windows while a self-employed driver uses a Mac at home, and a Linux machine may be the spare laptop that goes in the cab. With shared files, the person who plans and the person who drives can use whatever they have.
It also helps over time. Changing computers should not mean losing the rounds you have built up. Saved routes and address lists are ordinary files you can copy to the new machine.
Space and memory on any system
Map regions take space and preparation needs memory on any system. A county is a few megabytes and prepares in seconds to minutes; Great Britain is about 2 GB to download and needs roughly 8 GB of free memory to prepare. Plan accordingly on a laptop with less to spare.
As on Windows, Route has no account, API key or paid map service, and no live traffic, since everything runs locally. UK postcodes come from OS Code-Point Open and cover Great Britain only.
Moving across from Windows
Download the version for your system, choose a region, and once it is prepared, open a saved .ozroute file or start a new route. If you already plan on Windows, copy your saved routes across and carry on where you left off.
Whichever computer is to hand, Route by Zaweba plans the same way, offline and with the same files.