How do I make URL rewrite work with web.Release.config transform?

Transformation will only happen if you put proper xdt attributes on the elements that need to be transformed. Try adding an xdt:Transform attribute to your release config:

<system.webServer xdt:Transform="Replace">
    <!-- the rest of your element goes here -->
</system.webServer>

That will tell the transformation engine that the entire system.webServer element from Web.config needs to be replaced with the one from Web.Release.config.

The transformation engine will silently ignore any elements that do not have xdt attributes.

Obligatory link to MSDN.