Windows 10 S Can’t Run Linux Distros Available From Windows Store
Microsoft's Rich Turner cleared up the confusion in a blog post. He notes that just because an app is available in the Windows Store does not automatically mean that it is safe and suitable for running in Windows 10 S. Microsoft previously stated that Windows 10 S is "streamlined for security and superior performance," and with regards to the former, users will find that all command-line apps, shells, and consoles are blocked.
Outside of security concerns, Microsoft points out that Windows 10 S is supposed to be as easy to use as possible.
"Windows 10 S is primarily aimed at non-technical users – teachers & grade-school children, non-technical students, content creators, artists, etc. – people who don’t typically want to spend time & effort futzing with their PC – people who just expect their computer to work safely, quickly, reliably and efficiently," Turner says.

Windows 10 S represents Microsoft's attempt to lure students and teachers back into its ecosystem with an OS that is just as easy to use. To that end, it is understandable why Microsoft might choose to block some apps, including Linux distros. However, it's not just Linux that Microsoft is keeping at arm's length.
Turner points out that Windows 10 S is not ideally suited for app developers, hackers, admins, and IT pros who typically need tools that have access to low-level features. He's talking about things like debuggers, registry access, file system access, low-level hardware resources, and so forth.
One thing to keep in mind is that Microsoft will allow Windows 10 S owners to upgrade to Windows 10 for $49. So if a user really wants to install Linux, there's an upgrade path available.