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I would compare this with the players and the coach because the coach tells the players what to do like the president in the executive branch, but the coach doesn't have all the power and they have to often check with the players because they are the ones running the play. Another way of looking at this would be that there isn't a dominant player on the court all the players help and communicate with each other.

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Like how the team has an owner and the coach follows his/her rules but can also make their own

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The executive branch is like the out of bounds line because it sets limits

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Individual rights in basketball would be a specific player having the freedom to decide whether to take the shot, or drive for the layup or pass it to someone else, and now that person has the freedom to do whatever they think it's best.

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This in basketball would be like how the point guard decides to do the play or not, but they can't make that decision if his/her teammates don't agree.

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The referees are like the judicial branch because they interpret the rule book just like the judicial branch interprets the constitution.

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This would be the basketball, because without it, there is no game, just like how without the legislative branch there would be no laws and everything would be chaotic.

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These are like basketball referees, there are always two on the court, making all kinds of calls, they both have the same amount of power though, if they didn't, then why would we even need two? just give us the one with the most power then right? well, no. This wouldn't be fair because the referee might be biased, but if there are two with the same power, they can discuss things and make the calls fair.

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Limited government in basketball would be like the referees, the parents and the coach. The referees have the freedom to make the calls, while the parents and the coach verify if the call was necessary or if the ref faked it. The parents are there to watch, but when it gets heated, sometimes it gets out of hand and they might yell at the referees, so the coach is there to set boundaries. The coach is there to coach, not to play, so when the coach steps on the court, the ref can tell them to back off. They keep each other in check.

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I don't really have a good analogy for this but I would say that republicanism in basketball would be a commitment to the sport of basketball and it is a lifestyle, like, you don't just practice when you are with your coach and you don't just play when you have a game. You practice when no one is watching, you play with your friends whenever you can to get extra practice, you put the work in, you eat healthy, etc. Just like how For them, republicanism isn't just a form of government. It is a way of life and ideology.