Strickland doesn't like McFlys because no McFly has ever amounted to anything in the history of Hill Valley. George McFly has no confidence and allows others to walk all over him. Thirty years later, his son Marty has no respect for the rules. He doesn't like Biff Tannen because he's a bully and his ancestor killed his grandfather. Maybe.
In 1885, at the end of the gunfight between Marty and Buford Tannen, "Mad Dog" is arrested for robbing the Pine City stagecoach. He was arrested by the Deputy Marshall. But haven't you ever wondered where Marshall Strickland was? Why wouldn't the Marshall be there to make the arrest himself? Well, it's not in the final film, but there is a deleted scene from Part Three where Buford Tannen shoots Marshall Strickland in the back.
The scene was removed because it was deemed too dark for a comedy. It was also removed because the filmmakers thought that the murder of a lawman would most likely result in Buford's execution. If Buford Tannen was executed, he wouldn't produce any offspring and therefore no future Biffs would be born. In a single universe/single timeline, his arrest for the robbery would stand to correct any error in timeline continuity.
But it is part of the story. It just wasn't featured. There was only one witness, that being Marshall Strickland's son. Quite possibly word had not yet reached the Deputy Marshall in Hill Valley. This justifies the reasoning for the Deputy Marshall making the arrest and the charge being the robbery of the stagecoach.
However, this is the third 1885. The first being the original, unaltered 1885. The second was altered by the existence of Doc Brown. The third 1885 was altered by Marty and the Doc. As far as we can know, the murder of Marshall Strickland by Buford Tannen never occurred in the first two universes. The only reason Tannen was on his way in to town that day was to shoot Marty in the gunfight. The only reason the Marshall rode out to meet Tannen was to stop him from having a gunfight with Marty.
Marty McFly is the reason Strickland's ancestor was murdered. In the original 1885, he may have been just a stagecoach robber and town menace. In the second 1885, he murders Doc Brown over a matter of $80. Because of Marty's existence in the third 1885, Tannen murders a lawman. Because of this, he may have been executed. The filmmaker's explanation for the omitted scene is irrelevant. There are no future Biffs.
Once Marty finishes his time travel to his final 1985, the third created and the fourth overall, we never see another Biff. We never explore this 1985 very far, but it is very possible there are no Biffs. Needle's there, sure. Potentially two Martys, two Jennifers, and another Doc and DeLorean. And potentially a Biff if Buford was able to procreate before his death.
We know Marshall Strickland had a son. So Principal Strickland might be around, too. He just might really dislike Clint Eastwood movies.