they might be blocking wpsite.com/xmlrpc.php on apache config level you have no access on shared hostings and this in htaccess might be something that it is needed after that.
try this url on your wp site wpsite.com/xmlrpc.php and see outcome if output is blank of forbidden than access to xnlrpc.php file was denied but if you see
XML-RPC server accepts POST requests only.
than it is something else and my opinion is that you should consider deny access to xmlrpc.php on every wp unless you use it but anyway if you are using it you have ability to give access to IP's of other sites you use for api access and deny to generic public
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