That screenshot from
that post did not state that a camera is an extension of the eyes in any legal sense. There is more context on the page where I think you took the screenshot from:
Photographers
If you go down the page further, there are exceptions to the "if you can see it, you can shoot it" rule.
That would directly speak to your comments about taking pictures of a woman breastfeeding without consent.
There are other exceptions to that rule. There are plenty of public places in the US where you can not take a picture. Courtrooms are one example. You can't take photos in the Pentagon.
There is also a big difference between taking a picture for personal enjoyment as opposed to commercial use. That page did not address any of that.