Your program makes an SMTP connection to the sendmail server. If you own this server, you control its configuration. Nothing will be blocked.
Spam, however, is spam. Your customer might think their email is gold, but their customers might think it is spam. Oh good.
First, you need to make your email campaign "enter." If customers want to receive email notifications, they request. If they do not request, they do not receive email.
Secondly, you need to record the bounce you receive from the provided email address. Hard bounces come back with answers like "no such address" in various forms. Soft bounces - "we're still trying or mailbox." You must judge what to do with the bounces.
What about the best you can do. You cannot make people admit that your customer email is really important, but the other spam is just spam.
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