There is no question Beavis and Butthead had a large long term influence on the 90s. Their radical views and way of life influenced a lot of people. It even had a large influence on those that didn't watch them but still detested them. They are a type of show that comes a long once in a generation.
Beavis and Butthead did have a long-term influence on 90's culture. People who watched the show still remember the catchphrases. You can still see episodes on Youtube. If you google them, you'll find pages and pages of results. As recently as this past January, series creator Mike Judge was asked in an interview about new episodes of the series. So the show has had a long-term influence.
Yes, Beavis and Butthead had long-term influence on the 90s generation, because they were extremely popular and they were remembered so well by that generation. People mimicked sketches of the pair, and tried to emulate their comedy. There were many derivative works. Beavis and Butthead had a great deal of influence on the 90s generation.
I do not believe a year has gone by since my childhood that has lacked at least one conversation about Beavis and Butthead. I do not believe he cartoon had a long-term influence on the 90's generation. Being born in the 80's and being old enough to watch it when it aired, I didn't care for it. I was a girl, so Daria was what I watched. While the men of my age loved Beavis and Butthead and may have mimicked the show from time to time, I don't believe it overly influenced their behavior. Thankfully.
Beavis and Butthead did not have long-term influence on the 90s generation. Most people back then just saw it as a cartoon just like South Park. It was watched frequently but when it was taken off the air I do not think that many people missed it. I do not think it had a long-term influence on the 90s generation.