You are correct that money doesn't enter into it (at least directly).
The Dean Martin paraphrase however is not quit correct. Having EU people on your mailing list does not necessarily make you subject to GDPR. It depends on where you are, and possibly on your intent.
The territorial rules for GDPR are:
1. It applies if you are in the Union, regardless of where the people on your mailing list are and regardless of whether processing their data takes place in the Union or not.
2. If you are not in the Union, GDPR applies to the processing of data of people in the Union where the processing activities are related to ...
2a. ... the offering of goods or services (regardless of whether payment is required or not) to people in the Union, or
2b. ... the monitoring of the behavior as far as their behavior takes place within the Union.
Whether or not you are offering goods or services to people in the Union depends on whether you envisage to do so. The mere accessibility of your website from the Union is not sufficient.
For example if you were running a mailing list for your small city's chess club and someone in the EU found your site and signed up, you probably would not have any GDPR obligations to them.
If your chess club site also sold chess equipment that still probably wouldn't be enough unless you did something to indicate that you were actually trying to include EU. For example if your site had localization for all major EU languages, gave pricing in both dollars and Euros, and included VAT you would be covered by GDPR.
But if the site is only in English (and maybe Spanish), gives pricing in dollars and only accepts dollars, only collects US sales taxes, only ships via USPS, and doesn't have anything that indicates you might be catering to EU people, you are probably in the clear.