How is it sustainable for AMD to maintain their software on Linux for free? Would you maintain your own Linux software (and its distros) for $0? I see no problem with monetizing Linux users. If I am monetizing Windows and macOS users, there should be no exceptions towards Linux especially as Linux support is always ill defined (there are hundreds of distros to support and test.)
1: The software is not free. There is what essentially amounts to a free trial. This free trial used to support Windows and Linux. Now the free version only supports Windows, only the paid tiers work on Linux.
2: The software is what amounts to a hardware-specific compiler/IDE. AMD sells the hardware, with healthy margins. Asking "how is it sustainable for AMD to maintain [Vivado] .. for free" is the same as asking, "how is it sustainable for AMD to maintain their OpenGL drivers for free". They have a solid revenue stream from hardware sales that's enabled by the software.
3: Maintaining a free Linux version is close to 0 additional cost. They already need to maintain a free tier because they provide that to Windows, they already need to maintain Linux support because they provide that for the paid tiers. The only extra maintenance would be whatever edge case bugs occur only on the free tier and only when compiled for Linux.