Here is a list of thing of things to consider. Feel free to add to it.

The Beatles
psychedelic music
Led Zeppelin
disco
punk rock
arena rock
Huey Lewis and the News
Family Ties
Michael J Fox
Christopher Lloyd
Stephen Spielburg
Ronald Reagan

Here is what I've figured out for some of them. I think The Beatles and psychedelic music would still be around in the 1960s in the BTTF Universe. Led Zeppelin would probably be the same, and they never were political in their music. About the closest they really went to being political was with Immigrant Song. It probably wasn't until the 1970s that Biff started to become powerful enough to influence world politics. Arena rock probably would not catch on as much in the Biffhorrific timeline, while punk and heavy metal may catch on a little more. Family Ties would probably not exist in the Biffhorrific timeline. For some reason, the idea of Alex P Keaton being a Biff Tannen worshipper doesn't sit too well with me. Disco would probably die out even sooner in the Biffhorrific timeline, if it even has a chance to get started. Huey Lewis would probably form a different band in Canada, and become Huey Lewis and The Rebels. Michael J Fox would probably be too afraid to enter the US, with Biff being so powerful and corrupt - and Christopher Lloyd might decide to leave the US. Actually, I said that Michael J Fox went to Switzerland - and became friendly with Marty McFly. With Stephen Spielburg, it would be a hard call - and, as for Ronald Reagan, it would be hard to determine if he would be a Biff (and Nixon) supporter, or not.

I think all of the Beatles would be dead by 1985a. Biff probably would have personally sent men to shoot them. Led Zeppelin would be too scared to enter America. Family Ties would not exist. I think Rock music would be dead. Michael J. Fox would stay in Canada. Christopher Lloyd would have no career, at least not in acting. Steven Spielberg would not have been making movies, Biff would not allow Liberals in Hollywood. Reagan would probably still be governor of California.

What do you think the country music scene would be like? Rock music would probably be mostly underground in the US - and many Americans would probably escape to Canada, Europe, and Australia. It wouldn't just be the draft dodgers (the draft would probably still be in effect), but it would be everyone who disagreed with the Biff Tannen regime and was able to leave the country. Do you think there would be any safe places to live in the US? Do you think Canada, Europe, and Australia would be relatively safe? Michael J Fox may hear about Biff Tannen's stepson, Marty McFly - and be curious and concerned about this young boy who resembles him. Of course, he'd probably be concerned about Dave and Linda, as well! What about Sammy Hagar - and his song, I Can't Drive 55?

As for Sammy Hagar's song, it was only background music. No "alleged radio" was playing it. I think most Country Stars get the opportunity to perform at Biff's Pleasure Paradise. Others, also known as the liberal country stars, would escape to other countries.

What do you think about the whole Huey Lewis and The Rebels idea?

I like it. I can see their music being different though. Their music in real life is very upbeat, but I can see it being very loud and angry in Biffhorrific timeline.

Do you think Led Zeppelin would be any different in the Biffhorrific timeline?

I think it would be the same.

I think so, too! As they were never really political in their lyrics. Immigrant Song probably comes the closest.

I like to think most of the music would be the same, though.

Yeah, maybe I should write something on that someday - but not anytime soon. I personally think Lorraine would've shot Biff much sooner than 1996. Perhaps, not long after "our" Doc and Marty showed up in that world. I think things would eventually become more normal, which would explain why Hilldale didn't appear to be any different - after Old Biff came back to 2015.