> Isn’t it then your obligation to never visit that site again?

Not really. As long as your site is public, I can enter. If you don't want that, make it private, or subscription only.

> It’s like if you found out a restaurant didn’t accept cash and still kept going to eat there when you only had a credit card, knowing in advance you can’t and won’t pay.

It's more like going to a public museum that accepts donations and not making a donation. The place is public, and I decide if I pay or not.

No, how a website monetizes their site is not my concern. Just because they choose ads does not obligate me to decide to not go there again. In fact, due to my technology choices, I may never even realize they have chosen that route as I may never see their ads in the first place.

As a publicly available resource, it is like browsing. I can browse many brick and mortar stores without exchanging anything of value. And like a store, if a website decided they did not want people browsing without a purchase, they could block access.