I maintain three different projects for three business in .NET Core using Linux Docker containers and it's been very smooth.
The ability to have both C# and F# along with a ton of perfectly serviceable libraries is great.
I'm using ASP.NET Core for the web stack, swashbuckle to auto generate swagger docs, EF for auto generated database models. It's pretty great actually. Adding a new field is as easy as making a migration file, changing the API message, and adding one line to map the database model field to the message field. Everything just moves smoothly.
The resulting web servers just work. I've had effectively no issues with them at all. The only issues I've had were the result of Portainer not correctly shutting down a container, which really isn't related to .NET at all.