From the perspective of Kendo UI, this is a bit out of scope. Kendo UI is a solution for front-end development. It does not replace server-side technologies, like ASP.NET, Rails, or PHP. The same membership solutions you use with those frameworks today are applicable to Kendo UI. The only difference is the interaction (where you may rely more on services for authentication/data than on full-page round trips).
Same goes for data security. HTTPS, forms authentication, login-redirects- all of this still applies with Kendo UI, and in most cases the technique does not change.
So to your question: You build secure apps with Kendo UI the same way you always have. You just get a richer, more responsive front-end on top of that security.
Hope that helps.