JSFiddle - React, Tailwind, and code Playground

HTML

<body>
<div data-role="page" class="jqm-demos" id="pageMainForm">
	<div data-role="content" class="ui-content jqm-content">
		<div data-demo-html="true" data-demo-js="true" data-demo-css="true">
			<form>
				<select id="filter-menu" class="filterable-select" data-native-menu="false">
					<option value="Option 1">Option 1</option>
					<option value="Option 2">Option 2</option>
					<option value="Option 3">Option 3</option>
					<option value="Option 4">Option 4</option>
                    <option value="Option 5">Option 5</option>
                </select>
			</form>
		</div>
	</div><!-- /content -->
</div><!-- /page -->
</body>

CSS

.ui-selectmenu.ui-popup .ui-input-search {
	margin-left: .5em;
	margin-right: .5em;
}
.ui-selectmenu.ui-dialog .ui-content {
	padding-top: 0;
}
.ui-selectmenu.ui-dialog .ui-selectmenu-list {
	margin-top: 0;
}
.ui-selectmenu.ui-popup .ui-selectmenu-list li.ui-first-child .ui-btn {
	border-top-width: 1px;
	-webkit-border-radius: 0;
	border-radius: 0;
}
.ui-selectmenu.ui-dialog .ui-header {
	border-bottom-width: 1px;
}

JavaScript

( function( $ ) {
function pageIsSelectmenuDialog( page ) {
    var isDialog = false,
        id = page && page.attr( "id" );
    $( ".filterable-select" ).each( function() {
        if ( $( this ).attr( "id" ) + "-dialog" === id ) {
            isDialog = true;
            return false;
        }
    });
    return isDialog;
}
$.mobile.document
    // Upon creation of the select menu, we want to make use of the fact that the ID of the
    // listview it generates starts with the ID of the select menu itself, plus the suffix "-menu".
    // We retrieve the listview and insert a search input before it.
    .on( "selectmenucreate", ".filterable-select", function( event ) {
        var input,
            selectmenu = $( event.target ),
            list = $( "#" + selectmenu.attr( "id" ) + "-menu" ),
            form = list.jqmData( "filter-form" );
        // We store the generated form in a variable attached to the popup so we avoid creating a
        // second form/input field when the listview is destroyed/rebuilt during a refresh.
        if ( !form ) {
            input = $( "<input data-type='search'></input>" );
            form = $( "<form></form>" ).append( input );
            input.textinput();
            list
                .before( form )
                .jqmData( "filter-form", form ) ;
            form.jqmData( "listview", list );
        }
        // Instantiate a filterable widget on the newly created selectmenu widget and indicate that
        // the generated input form element is to be used for the filtering.
        selectmenu
            .filterable({
                input: input,
                children: "> option[value]"
            })
            // Rebuild the custom select menu's list items to reflect the results of the filtering
            // done on the select menu.
            .on( "filterablefilter", function() {
                selectmenu.selectmenu( "refresh" );
            });
    })
    // The custom select list may show up as...