This issue occurs when your site tries to load /wp-admin/admin-ajax.php file (probably loaded in the theme). I assume .htpasswd authorization was set up for /wp-admin/ directory.
It is possible that some of your theme or plugins got exploited (not necessarily). I would try disabling all plugins and enabling one by one to figure out what went wrong.
For more details you may google for: /wp-admin/admin-ajax.php authorization 301
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