Hi,
The issue you have there (which I was able to reproduce and study on your website but not on my end) is that when the AJAX request is done to refresh the filter module area, it contains only the HTML of the module. It doesn't contain the HTML header, etc. And the javascript to initialize the slider system is in the header. So it can't initialize the slider after it refreshes the area.
This indicates that there is an "exit" done to stop the processing of the page after the main area processing.
As I don't have such exit on my end, I'm thinking that because something else on your website see that we're using the parameter tmpl=raw in the URL to request the module's new HTML, it stops after the main area instead of letting Joomla finish the processing to add the header around.
This could could from a view override, but it could come from something else in your template (which is why I aksed you to try with the default template so that we can be sure whether it comes from the template or not), or a system plugin.