You have the right to say it, and I have the right to ignore it, because that's the way the Internet is implemented. You may pretend that it works differently, but until the day it works like broadcast TV, users will have the right to pull whatever content they want from servers.
They have all the right and power to refuse to give their content away for free. You have all the right and power not to look at their ads, to preemptively strip them from your view, or to modify the page you yourself will visualize in any way you see fit.
Think of newspapers given away for free on the streets. I can make whatever collage I want into what I received for free, it's absurd to insinuate my reading habit could constitute a crime.
Of course, since you're being given something for free, there might be cases where you're ethically compelled to retribute (in particular when you enjoy the content, believe it is useful, etc). But here you should be able to chose how to contribute -- if you're restricted to contribute only by viewing obnoxious ads I would say it's perfectly ethical to refuse to do so.
What I do is support the Patreon account of several content creators I enjoy. I know my little donation has an impact on them, enabling them to keep producing great content. Most websites that I find useful don't offer particularly compelling media of retribution, and I feel my cost to them isn't significant at all. The marginal cost of my usage of Google search engine to Google is quite small, I would guess thousands or millionths of a cent per query. I don't need to worry about donating to Google. They have other ways of generating revenue from me, like the query information itself, and other services like the Android App store.
This does seem to be the crux of our disagreement. You think that offering up your content merely represents a non-binding expectation. In other domains, we don't take that position. If I weave you a scarf, and I say "Hey, i'll give you this scarf if you go to the store and pick up some cough medicine for me", and then you take the scarf and refuse to go to the store for me on the grounds that I "merely had the expectation, but no guarantee that you would go to the store for me", that seems pretty odd. I'm curious:
A) Whether you believe these situations are different
And
B) If you believe they're different, why.