Simple - I don't watch scheduled TV (I either record it or watch it online via Hulu/Netflix/etc.) and magazine ads don't bother me because I can simply leaf through them. And, also, I don't read magazines that have too many random ads. Those that I do read either have relevant ads or have them nicely segregated so they don't bother me. I never saw a magazine that has an ad with auto-play video, high-frequency animations, auto-play sound or is placed in a way that makes other content unaccessible until I spend several minutes on it.
I don't know what I would do if I didn't have the modern options. Switch to DVD/reading books probably - that's what I did before I had DVR and online streaming.
I know that many sites rely on ads for their income stream. I do not feel an obligation to sacrifice my psychological well-being in order to make that model succeed. Fortunately, they seem to be doing just fine without me.