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LabVIEW
LabVIEW Linux and .NET Core
No and it likely never will. .Net Core is a limited subset of .Net on Windows, not a full replacement for it. Microsoft has no plans to fully open source the entire .Net system and likely couldn't even do it easily as it contains many parts that interface to proprietary parts of the Windows system that Microsoft won't just open like that.
The LabVIEW .Net interface was developed to the full .Net interface even if that was at that time .Net 2.0, and makes use of features that are not part of .Net Core. Porting this to .Net Core likely is not an option without loosing some functionality in the existing .Net functionality on Windows (such as the .Net container in the front panel).
Combine that with the fact that .Net Core is an even more moving target to shoot at in comparison to the Windows .Net API, and that LabVIEW for Linux is a margin product in comparison to the Windows installation base and even more so in comparison to sales (lots of LabVIEW for Linux sites use an educational license that brings in only a fraction of the sales per license than commercial licenses) and you get a situation where a manager in a company that has to report to its shareholders, has to have suicidal tendencies to suggest such a change.
I agree, small change it will ever happen.
If it helps, I could live without the .NET FP container. If that is the showstopper, dropping it would be acceptable for me.
Search LabVIEW like a graph! 
@Matthew.L wrote:
Maybe I am just the minority 😊
I'd say almost every user would like that.
Still, I don't see it happening soon...
Actually .Net Core for NI Linux RT has a verey small change to be done. It would be non-trivial to implement for sure, but NI "owns" the platform and can dictate which exact .Net Core package should be installed with each version (NI Linux RT is basically versioned around LabVIEW releases with the public package version number the same as the according LabVIEW version you want to run on). This makes the whole manageable in terms of version compatibility.
They would have to add a compiled package of .Net Core to the opkg feed they use for each NI Linux RT version and of course port the .Net interface they use in LabVIEW for Windows to work properly with .Net Core. All of this is anything but trivial to do, means a lot of engineering hours and many more hours for testing, for something that some people believe would be beneficial but which I still have to see widespread adoption of. Use of .Net Core libraries may sound cool as it avoids the hassle of having to configure a few Call Library Nodes properly, but under Linux you can call shared libraries directly too with the Call Library Node, which results in a much more direct and efficient execution than having to invoke an entire .Net Core monster in your process to call a few external functions. And if all else fails you still can use SystemExec to call just about any system command directly. Many people feel that SystemExec is slow and connvoluted but this is how almost everything in Linux/Unix is done anyways. And invocation of command line programs under just about all Unix flavors are in fact lightweight and very fast in comparison to Windows. The Windows process model is pretty heavy weight and creation of a new process, even if it does not involve a GUI, is expensive and this is another reason that DLLs got so popular under Windows since it allowed to add functionality to a program without having to invoke child processes over and over again. Then there came OLE, later ActiveX and finally .Net which were all supposed to make invocation of external components easier and I'm waiting already for the next technology that obsoletes .Net. 
Trying to support .Net Core on normal Linux is simply never gonna happen. The binaray compatibility between versions is in proper Linux tradition repeatedly broken, so that you would be hunting down the right version that works with a particular LabVIEW version, that might or might not work with the particular glibc version and other libraries that the Linux distribution comes with. And then that .Net Core version you installed for LabVIEW might break with super duper app xyz that you also want to run on the same system.
No, and NI's stance on such things is:
No comment on future product features, neither about if they are at all in the works nor about any expected release date. Sometimes if you know someone in the knows and are willing to sign an NDA and offer your first born as well as both your hands for violations of that NDA, you may get some more off the record comments, but not more. 
