I believe Beavis and Butthead would still be considered controversial by today's television standards. I believe the only reason Beavis and Butthead made it to television was the fact that MTV was willing to do risky things opening the way for such programming. I believe it still raises eyebrows today.
The standards for what we regard to be obscenity on television have been lowered significantly since Beavis & Butthead's time, and the series is now comparatively tame compared to everything else on television, especially its own network, MTV. Beavis & Butthead's satire is comparatively tame compared to all of the shows that came in its wake.
Beavis and Butthead are only controversial and titillating to immature and uninformed people. The humor in Beavis and Butthead is actually quite sophisticated. The point of the program was not to make salacious remarks that were funny; it was a look at how today's youth is becoming lost. Outrage and what they said was made to seem far more important than their basic inability to grow up. The moral was that society will tolerate a loser and a leech, just so long as he doesn't use swear words or leer at pretty girls in public.
I can't think of a time when Beavis and Butthead were considered controversial by any standards. When they started on MTV originally, they were actually considered to be pretty original and funny, but typical of the content that you would find on that channel. I think the word you're actually looking for is "relevant" which, by today's standards, they're not.
Beavis and Butthead would not be controversial today on network television, let alone on cable or on some of the paid channels. A lot of the pseudo nudity and crass humor would easily be permitted for even younger children today, and it would not make too much noise if seen today.