Some email clients (particularly Gmail I think) are more sensitive to this sort of thing than others.
Marketing Pro has email authenticaton settings (also known as DKIM) that overcome the issue, but I do not think these are supported in Marketing Starter unfortunatly.
As the issue you are experiencing is specific to your account, I would recommend partnering with HubSpot Technical Support regarding this matter. They will be able to provide best next steps specific to your account and set up.
I got the same issue with the free account: Most of the Opt-In-Mails are not received by the contact. Is an authentication possible with starter? Otherwise I too see this whole subscirption as insufficient.
The DKIM authentication which is discussed in this thread is available for Marketing Hub Starter subscriptions and above. This knowledge base article explains the details so please feel free to check out.