Performing CRUD operations on front end in wordpress

Yes. You can do.
Try using ajax, or better? using wordpress rest api

Ajax method: need register your function and action to do

Simple example:

add_action( 'wp_ajax_my_action', 'my_action' );
add_action( 'wp_ajax_nopriv_my_action', 'my_action' );

function my_action() {
    return json_encode('hello word');
}

jQuery(document).ready(function() {
    var data = {
        'action': 'my_action'
    };
    jQuery.post(ajax_url, data, function(response) {
        alert(response);
    });
});

More info for ajax:
https://codex.wordpress.org/AJAX_in_Plugins

WordPress rest api: need to register a route

very simple example:

add_action( 'rest_api_init', function () {
  register_rest_route( 'yourName/v1', '/myroute', array(
    'methods' => 'POST',
    'callback' => 'my_function',
  ) );
} );

function my_function( $data ) {
  return 'Hello World';
}

jQuery(document).ready(function() {
    jQuery.post('/wp-json/yourName/v1/myroute', function(response) {
        alert(response);
    });
});

More info:
https://developer.wordpress.org/rest-api/