Hi, the plugin always sends emails, it has not filter on destination domain (of course). The problem is for sure your sending server which could be blacklist by few mail provider. Ask your provider to check your server against blacklists, to setup the SPF record for your domain.
You can even try a mail delivery service (mailjet, sparkpost, elasticemail) and see if with their service email are delivered. They almost surely will be.
Stefano.