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While I would have liked to have seen Mulcahy get a little beat-down or at least put in his place somewhat, I think a lot of what's going on in the film is the tension between military discipline and the racial division. One of the things the movie does really well, I think, is giving us a portrait of this stuff without commentary. For example: the unbelievably powerful scene where Trip gets lashings for desertion. In military discipline, this is standard, but it's entirely different with Trip's scars and history and the history of the men watching. It's a moment where Shaw realizes, "Mmm...maybe this isn't right." And he sees beyond his standard assumptions.

Within the men of the 54th, we see various ways that they handle the situation. Trip is all lip and rebellion. He's pure anger. Rawlins wants to blend in and become one people. But he's often at odds with himself and the others. Rawlins gets called an Uncle Tom by Trip because Rawlins is trying to get above all this crap and make peace and that's perceived as capitulation, sucking up, or weak by Trip.

So, the scene where Rawlins restrains Trip? That's part of that complexity.

On a practical level, Rawlins also knows that Trip will bring down military discipline and sow more seeds of discord if he fights Mulcahy. If Rawlins didn't stop Trip, it would have escalated further. After all, the order came from Shaw. They can't have division from bottom to top: the whole unit would rip apart.

Mulcahy was their drill sergeant. It was his job to be rough on the men in order to physically and mentally mold them into soldiers. Back then they were allowed to be more physical with the men, today not so much. But one thing still holds true, it would not be a wise move for a private to take a swing at his drill sergeant. No matter how justified it may have been, it would be the private facing disciplinary action.

That's boot camp. You will be verbally abused every single day.

The juice wasn’t worth the squeeze, Rawlins says so in so many words. Tripp would have been beaten to an inch of his life had he struck Mulcahy or possibly killed, Rawlins knew this and was looking out for him.
And as Trevorh said, this is infantry bootcamp, it’s no fucking joke, ask me how I know ; )