Did you ever see them fight over a seat? OMG just pick a different seat who gives a crap!
Well, it's not about the actual seat - It's about rights. Sure, finding another seat will solve the seating issue, but the kid's rights are still violated. That's why finding another seat doesn't solve the problem.
Children have almost no self-rights. Everything they have is provided to them by adults. We choose their food, we pick their clothing, and allow them possessions. We own their shelter, dictate their playtime, sleep time, screentime, even the words they can and can't say...And then they go to school where they are under even stricter rule.
This leads to a "Bottleneck of Resources."
Because kid's rights and resources are limited, they are extra sensitive about protecting the few that they have. These resources can include objects, spaces, attention, and privileges. This leads to increased competition for those rights and resources. And that's not all. When multiple people occupy the same role, such as siblings, competition between them is increased even more.
"So, what do I do?"
Be mindful of their situation. Just because it seems trivial to us doesn't mean it should be to them. We have rights, they don't.
Make extra sure that their personal spaces and properties are respected. It means more to them than you may think.
Respect "first come first serve" when appropriate.
When there is a "tie" - Use an arbitrary deciding device. Rock Paper Scissors works great because it rules out any favoritism or unfairness. Kids usually accept the outcome. 2 out of 3 also helps to reinforce the randomness and increase acceptance.
The "Seat Check" also reduces issues. When they get up from their seat with the intention of returning, they say "Seat Check!" Which officially holds it for them. (I know it sounds stupid, but it cuts down on the drama).
"You two will knock it off right now because I said so! You don't always get what you want so deal with it!"
If you feel that all of this stuff is over-pampering, you might be right. Just make sure that you understand the phenomenon that's going on first before doing what you have to do.
Summary
Sibling rivalry is the result of 2 (or more) kids in the same role, competing for limited resources.