Пример поиска

$('.shop2-filter__item').each(function () {
    let $this = $(this);
    let $checkbox = $this.find('.shop2-filter__checkbox');
    let $search = $this.find('.gr-multiselect_js .gr-multiselect__search');
    let $search2 = $this.find('.gr-multiselect-2_js .gr-multiselect-2__search');
    let searchWidth = $search.outerWidth();

    $search.on("keyup", function () {
        filtrate($(this).val().toLowerCase(), $checkbox, 'gr-multiselect_hide_item');

        let thisLength = $(this).val().length;

        $(this).css({
            "width": searchWidth + (thisLength * 10)
        });
    });

    if ($checkbox.length > shop2.my.gr_filter_multiselect_count) {
        let $container = $(this).find('.gr-multiselect-2__container');
        $container.addClass('show_multi_search');
    };

    $search2.on("keyup", function () {
        if ($(this).val() != "") {
            $(this).addClass('active');
        } else {
            $(this).removeClass('active');
        };
        filtrate($(this).val().toLowerCase(), $checkbox, 'gr-multiselect-2_hide_item');
    });
});


function filtrate(searched, $context, hideClass) {
    $context.removeClass(hideClass);

    $context.each(function () {
        var isHidden = $(this).data('content').toString().toLowerCase().indexOf(searched) > -1;

        if (!isHidden) {
            $(this).addClass(hideClass);
        };
    });
};