Edit your globalTemplate and after the final {{endif}} but before the closing > on the BODY line:
<body class='ipsApp ipsApp_front {{if isset( \IPS\Request::i()->cookie['hasJS'] )}}ipsJS_has{{else}}ipsJS_none{{endif}} ipsClearfix{{foreach output.bodyClasses as $class}} {$class}{{endforeach}}' {{if output.globalControllers}}data-controller='{expression="implode( ',', output.globalControllers )"}'{{endif}} {{if isset( output.inlineMessage )}}data-message="{expression="output.inlineMessage"}"{{endif}} data-pageApp='{$location['app']}' data-pageLocation='front' data-pageModule='{$location['module']}' data-pageController='{$location['controller']}' {{if isset( \IPS\Request::i()->id )}}data-pageID='{expression="(int) \IPS\Request::i()->id"}'{{endif}} {{if isset( \IPS\Dispatcher::i()->dispatcherController ) AND !\IPS\Dispatcher::i()->dispatcherController->isContentPage }}data-nocontent{{endif}} {{if output.pageName}}data-pageName="{expression="output.pageName"}"{{endif}}>
Add the following (space at start, important)
{{if ISSET(\IPS\Request::i()->cookie["forum_view"])}}data-forumView='{expression="\IPS\Request::i()->cookie['forum_view']"}'{{endif}}
You now have an additional selector you can use called "data-forumView" which will contain either table, list or fluid
<body class='ipsApp ipsApp_front {{if isset( \IPS\Request::i()->cookie['hasJS'] )}}ipsJS_has{{else}}ipsJS_none{{endif}} ipsClearfix{{foreach output.bodyClasses as $class}} {$class}{{endforeach}}' {{if output.globalControllers}}data-controller='{expression="implode( ',', output.globalControllers )"}'{{endif}} {{if isset( output.inlineMessage )}}data-message="{expression="output.inlineMessage"}"{{endif}} data-pageApp='{$location['app']}' data-pageLocation='front' data-pageModule='{$location['module']}' data-pageController='{$location['controller']}' {{if isset( \IPS\Request::i()->id )}}data-pageID='{expression="(int) \IPS\Request::i()->id"}'{{endif}} {{if isset( \IPS\Dispatcher::i()->dispatcherController ) AND !\IPS\Dispatcher::i()->dispatcherController->isContentPage }}data-nocontent{{endif}} {{if output.pageName}}data-pageName="{expression="output.pageName"}"{{endif}} {{if ISSET(\IPS\Request::i()->cookie["forum_view"])}}data-forumView='{expression="\IPS\Request::i()->cookie['forum_view']"}'{{endif}}>