While support of .NET Core for SharePoint CSOM libraries on its own way (still no ETA), you can create a SharePoint add-in with ASP.NET Core 2.1 today. Of course, it adds some inconveniences, but at least you can target the latest version of ASP.NET. I’ve created a sample project at GitHub here so you can easily try it. This post describes how to configure everything to run it.

First of all, a few drawbacks worth mentioning:

- you can’t use F5 experience in Visual Studio for convenient debugging. Instead, you should manually upload your app into a site and attach Visual Studio to running web application.

- you can’t target a project to netcoreapp. Obviously you can’t do it because SharePoint CSOM for .NET Core is not available yet. That’s why you have to retarget your project to .NET Framework instead. Which means that you lose cross platform feature. If that’s essential thing for you, then you should wait for official .NET Core support. 

- solution described here only works for SharePoint Online. On-premises is a completely different story and out of the scope of the post

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