.NET Core is totally fine for playing around or for small apps and services.
It's usually for large projects that these backwards compatibility issues tend to crop up and be show-stoppers. You're likely better off with Mono in that case.
We've built our entire backend on .NET Core. We've got a lot of moving parts. The main pain points have ironically been certain Azure libraries which haven't been ported to the standard yet. I've also been using F# core and while the experience isn't yet there, it feels close.