The fundamental stoic concept is being able to distinguish things that are in our control and things that are out of our control. For things out of our control, obviously there is nothing we can do about them (these are indifferents). For example, the weather, earthquakes, major world events, etc. The only thing we can control are our attitudes - this is essentially the Discipline of Assent.
When it comes to people, we have an obligation to work with others - just as the upper and lower jaws need to work together, we too must work with other people. We ought to treat others with respect and justice - this is essentially the Discipline of Action.
In the passage above, Marcus hits on both the Discipline of Assent and Action. He wants to work well with others AND he wants to keep his inner peace (he wants to maintain a good attitude). Therefore, when Marcus wakes up in the morning, he is preparing himself to encounter grumpy, grouchy, Type A, mean, angry people. Before he even encounters them, he (in a sense) forgives them and vows that he will not act that way (since he knows people are meant to work with each other and we all share a divinity) AND he will do his best to work with them.
Practically speaking, what do you do when you meet someone who is mean or grumpy? For my part, I try to give them the benefit of the doubt - which means I try to kindly excuse their behavior. For example, a manager at work is in a bad mood - I'll chalk that up to maybe he didn't get enough sleep the night before or maybe he's hungry. I simply assume that this isn't his real self and that he'll be in a better mood later.
A couple of years ago, a co-worker of mine was working on a presentation with a manager. The manager is almost always really nice, jovial and easy to get along with. But on this day, he was a grumpy bear! My co-worker didn't know what the deal was. A couple of hours later (after lunch), the manager met again with my co-worker and the manager was back to his normal, happy self! As we talked about this, we concluded he was just "hangry" and needed some food.
As a follow-up, I bought my co-worker a Snickers bar with a "Grouchy" wrapper and we keep it around in case of an emergency when a manager is "hangry" :-)
more commentary in The Inner Citadel p. 207-208