I'm not certain I'd still call them a "startup" but they have been very open about their large use of .NET and the advantages it brings to bear.
[1] http://nickcraver.com/blog/2016/02/17/stack-overflow-the-arc...
Edit: More .NET information / usage.
[2] http://nickcraver.com/blog/2016/03/29/stack-overflow-the-har...
[3] http://nickcraver.com/blog/2016/05/03/stack-overflow-how-we-...
That said, we do maintain a number of .net libraries, such as Dapper or miniprofiler and we ported them to .net core (or we are in the process of doing that).
We are also contributing significantly, together with other community leaders, to the design and development of the .net core API.
This said, we have been having some of the pain that is mentioned in other threads. The framework is still incomplete and evolving, although a lot of what's coming out is excellent and very fast/modern.