As people get more used to it, advertisers just work harder and harder to sneak under the radar. We might get more self aware, but if anything it just leads us to be cynical and untrusting of things that are sincere.
The end result is likely a belief that there are two and only two kinds of media:
Insincere media where I can see that I'm being advertised to.
Insincere media that has outsmarted me and where I can't see that I'm being advertised to.
On a practical note, reputation works in this circumstances: if I read a piece about, I don't know, fruit jam industry in NYT, it's likely not a blatant paid ad. This is what they monetize when selling subscriptions; should they stop, their reputation, and with it the subscription revenue, would go down.