Creating a fake JavaScript exposed filter in Drupal 7 Views module
Here is the solution I used:

I created a new module named "My Views' Client Side Filters".

In the module's .module file I added:

&lt;?php

function my_views_client_side_filters_form_views_exposed_form_alter(&amp;$form, &amp;$form_state, $form_id)
{
    $form['#attributes']['onsubmit'] = 'return exposedFilterOnSubmit();';
    drupal_add_js('sites/all/themes/MY_THEME/js/MY_JS_FILE.js');
}


Which resulted in the HTML:

&lt;form onsubmit="return exposedFilterOnSubmit();" action="MY FORM DESTINATION" method="get"&gt;


And sites/all/themes/MY_THEME/js/MY_JS_FILE.js:

function isEmpty(str) {
    return (str.length === 0 || !str.trim());
}
var departmentAllShown = true;
var nameAllShown = true;
(function ($) {
    function reloadNames(name) {
        $('.views-row').each(function() {
            if($(this).find('.doctors_view_row_title').text().toLowerCase().indexOf(name.toLowerCase()) &gt;= 0)
                $(this).css('display','block');
            else
                $(this).css('display','none');
        });
        nameAllShown = false;
    }
    jQuery.extend({
        exposedFilterHider: function()
        {
            //Handle url (JavaScript only now enabled)
            if(!isEmpty(window.location.search))
                location = "MY_SITE_LOCATION/FORM_PAGE";

            var department = $('#edit-field-department-value')[0].value;
            var departmentIndex = $('#edit-field-department-value')[0].selectedIndex;
            var name = $('#edit-title')[0].value;

            var nameIsEmpty = isEmpty(name);

            if (departmentIndex != 0)
            {
                $('.item-list').each(function() {
                    if ($(this).children().first().text() === department)
                    {
                        $(this).css('display','block');
                        if (!nameIsEmpty)
                            reloadNames(name);
                        else
                            if (!nameAllShown)
                            {
                                $('.views-row').css('display','block');
                                nameAllShown = true;
                            }
                    }
                    else
                        $(this).css('display','none');
                });
                departmentAllShown = false;
            }
            else
            {
                //Enable all categories if not already
                if (!departmentAllShown)
                {
                    $('.item-list').css('display','block');
                    departmentAllShown = true;
                }

                if (!nameIsEmpty)
                    reloadNames(name);
                else //Enable all names if not already
                    if (!nameAllShown)
                    {
                        $('.views-row').css('display','block');
                        nameAllShown = true;
                    }
            }
        }
    });
})(jQuery);

function exposedFilterOnSubmit()
{
    jQuery.exposedFilterHider();
    return false;
}


Sorry I don't explain any further, I'm kind of stressed in time. If someone asks a specific question I promise to answer.

Hope this helps anyone!

BTW, although the code is a bit long it works spectacularly and runs swiftly.

Remember to change the classes! You might need to change things a bit since my layout may not be the same as yours.

My classes:

.views-row - Entire "person" row (The name container is somewhere inside and there are a few of those in every category)

.doctors_view_row_title - Name container

.item-list - The category container

Good luck guys!