Access WordPress User data to login/register through App REST

Solution:

Well WordPress it self has a communication protocol which is XML-RPC you can read more on it here, However it does not have authentication method builtin.

But you can try it some thing like this:

function mynamespace_getUserID( $args ) {
    global $wp_xmlrpc_server;
    $wp_xmlrpc_server->escape( $args );

    $blog_id  = $args[0];
    $username = $args[1];
    $password = $args[2];

    if ( ! $user = $wp_xmlrpc_server->login( $username, $password ) )
        return $wp_xmlrpc_server->error;

    return $user->ID;    
}

function mynamespace_new_xmlrpc_methods( $methods ) {
    $methods['mynamespace.getUserID'] = 'mynamespace_getUserID';
    return $methods;   
}
add_filter( 'xmlrpc_methods', 'mynamespace_new_xmlrpc_methods');

You can read more on Extending XML-RPC here. If you are using client side language for authentication, then you can check WordPress XmlRpc Javascript Api