I agree there are some parallels between ad-blocking and piracy (though they do tend to be in the realm of the "piracy = theft" idea rather than copyright-related parallels).
However, I think it's also important to recognize that by similarly-strong analogy, advertisements in general are inherently a sort of mental manipulation or brainwashing.
Now, I'm not saying that mental manipulation is inherently a bad or evil thing. When I'm writing this post, I hope that those reading it will become in some way more mentally accepting of my point of view. But I think we don't look enough at how susceptible we are to advertising, and how much advertising depends on exploiting cognitive biases or implying untruths that are not explicitly stated.
We (humans) are really bad at not being affected by advertising, even if we know we're being advertised to, and even if we know the ad is deceptive. When sites depend on ad revenue, they're saying "We're offering this content for free, but in exchange we want to be able to bias/prime your brain so that when you see Product X, even far in the future, you are more likely to desire it." That's a very powerful thing, and while it's certainly necessary for many business models today, I think we should think of this as a "necessary evil."
There are sites where I disable ad-blocking, often in response to a genuine plea on the part of the website. If it's a site I particularly care about and feel that I trust, then I allow ads as a way of helping them out. But if ad-blocking is piracy, then ads themselves are brainwashing -- exploiting failings in human cognition to unconsciously guide people into actions or purchases that may or may not be optimal for them -- and with the subject having limited defenses against it once infected.