Is it risky to install software that extends the OS login screen?

Not really. In the past, with the Windows GINA infrastructure in Windows XP and earlier, login screen extensions had to be chained together and a fault in one could render the entire OS inoperable. In modern editions of Windows and in other modern operating systems, there is a mature extension framework for the login screen, where failure in one package does not block logins in general. All versions of Windows starting with Vista use the Credential Provider framework and no longer have a GINA, so are safe to extend. See more at: https://hitachi-id.com