I would like to say that people no longer fight for no reason or let their tempers get the best of them, or are ruled by affiliation and association loyalties more than logic, but this is not the case. Tybalt believed that it was more important to be tough and to make sure everyone else knew he was tough, and he paid the price.
Tybalt was a bully. There always have been and always will be bullies. Tybalt showed he was a bully when he got upset at the Capulet ball by Romeo’s mere presence there. His uncle was not amused.
It fits, when such a villain is a guest:
I'll not endure him.
He shall be endured:
What, goodman boy! I say, he shall: go to;
Am I the master here, or you? go to.
You'll not endure him! God shall mend my soul! (Act 1, Scene 5)
Capulet called him a “saucy boy” and told him to leave off. He was not allowed to fight Romeo there, but he did not give up. He refused to give up. This goes beyond holding a grudge. This is someone who is taking advantage of a family feud to use a violent personality. Tybalt did not need to force Romeo to fight him, and if he hadn't, neither Mercutio nor Tybalt would have been dead (to say nothing of Romeo and Juliet's suicides later, which were directly related to Romeo's banishment).
We live in a violent world. Family feuds are not that common today. It is gang wars and border disputes. The motivation is the same though. Tybalt had no personal dispute with Romeo. He did not know him personally. He hated him because of his family name and where he was from. Hate is not something we left behind in Elizabethan England.