.NET is their own thing to begin with and nobody suggests rewriting core pieces of Linux with it. It would be more accurate to say, based on the reports of .NET working better on Linux than on Windows, that they're promoting the embracing and extending of their own Windows ecosystem by the Linux ecosystem, because they feel that they'd benefit more on balance from keeping those customers on .NET and using Azure than they would by keeping them in the Windows ecosystem which is probably a lost cause anyway.
Yet. But on a few distros it was heavily encroaching on default installed GUI applications. I don't know if that's increased recently because I've been straight Debian for 5 years now, but there's not a huge jump from that to the rest of userland.
edit: I think Miguel de Icaza was responsible for a lot of that incursion, and he seems to be drifting into the EEE interpretation of MS handling of .NET, too: https://news.ycombinator.com/item?id=31761130