The pieces you mentioned are either all on the Microsoft stack or irrelevant to it. jQuery and github, for example, have nothing to do with your backend's stack.
You do realize that C# in VS is just a compiler? It's csc.exe. There's no reason you can't host it in Eclipse. In fact there are several 3rd party components that allow you to host a C# editor anywhere you like.
The problem, in this case at least, is that the C# experience is so solid that the motivation to create an Eclipse one is pretty low. Maybe the Mono folks have something for it. But the amount of work that MS has done for the C# experience is truly impressive. I can, and have, written C# programs in vim, but it's not something I'd like to do on a regular basis.
I personally can't see myself using Eclipse on purpose again.
Microsoft has tools for test automation, but many people use nUnit because it's better. Microsoft has automated refactoring tools, but many people use ReSharper because it's better. Microsoft has source control tools, but many people use git/hg because they're better.
I've known people who do C# development with Eclipse. It's not as nicely integrated, but whatever. Nothing in the backend stack enforces your IDE tools.
It's the same with postgres or MySql. I personally don't use them because I prefer SQL Server. But I'm not tied to SQL Server by anything but affection for it because it works really really well for what I need.
I can't speak to nginx as I have no experience with it.