This is a very broad topic, because imo it goes to the very core of our psyche.
There are obviously some very simple considerations, like availability. If one person is available earlier, then it's very logical that the activity will be done first with the person that's available earlier.
Of course, that's not always the case, and there's still the question of "who do you ask first".
The main question is, what is "better"? I like gaming with a specific person more than another person. Is it better or worse that I ask that person first? I definitely apply a value judgement in this process. The one person has funny reactions to the games, which I like. The other person is more calm but very thoughtful and also very fun to game with. But if I was given a choice that I could only play with the one or the other, then I would choose the first person for gaming. This is a direct comparison for one quality in a person that one person "wins".
Is the other person now a worse person that I like less? Of course not. People have different qualities and it's completely normal that these qualities make them more suited for particular things. As a result, everyone is treated slightly differently. This is happening with everyone in every relationship in every situation in different degrees. Sometimes there is no preference, sometimes the preference is greater.
Now, for the "choosing" person there isn't that big of a dilemma. It's more impactful for the one that is asked first/later, the one "being chosen", because they implicitly recognize the value judgement that the first person made.
It's important to recognize that there is a possibility this value judgement is happening. Of course, sometimes it's based on randomness or availability, but it's more often simple reality that you like to do certain things more with certain people.
But many people deny this, or want to not think about it, to not "hurt other's feelings". But it is possible to talk about this openly (like anything lol). Being cognizant and open and honest about it is the first step.
So, what is your specific situation? Is a thing being done first with someone because there's actually a preference? Because if not, this can just be communicated and theoretically there shouldn't be a problem, since everyone will get to be "first" eventually, through sheer randomness.
If there is a preference, the "problem" is the involved person's egos. Humans are possessive and jealous by nature. It makes sense, because we live in a reality with limited resources. Everyone has a limited amount of time to spend. In an ancestral (and even today's) environment, survival depends on raising children. Theoretically, the more children/people you divide your resources (including attention/care) towards, the less likely the survival/flourishing of individual children gets. Even if we rationally decide to not have children or similar, the traits governing this behavior don't suddenly deactivate. Thus these traits also affect situations like "doing something first with someone".
I know what community this is in, and I recognize most people here already understand this. But the fact of this being a "separate" topic made me think it's worth repeating some of these thoughts.
In the end, the solution is the same. Relationships are naturally some kind of competition and do have differences, but we chose to disregard these, or rather, embrace them. We understand that it's possible to be with multiple people. But we must also understand that there are whims, preferences, inclinations.
So, I think "first" is "special" in some way, sometimes. But this doesn't destroy anything. It doesn't need to be a problem. It is possible to accept not being the "first", even when it's based on preference.
First, we have to understand all this rationally. Then we must talk about it like this so everyone has the same understanding.
Then, when the toxic/problematic thing starts, we need to recognize it. It's hard to do it personally, but we can try, and also, we can help each other recognize it. It's easier to recognize the problematic behavior in another person, an outside perspective makes it easier. The outside person can kindly remind/point out the problematic behavior, making sure to remember that this is a cooperative, beneficial thing for everyone.
When the behavior is recognized, then mindfulness can be established. You can try to observe your thoughts/behaviors and remember your preferred thoughts/behaviors. It is then possible to let the problematic behavior go. And replace it with the desired thoughts/behaviors. Meditation practice helps with this.
When you start with all this, it is hard to do all this, but with practice, it gets easier. And if you do it a lot, this aligns your subconscious with your conscious behavior.