In addition to the cogent points that by his very actions Atticus Finch, does, indeed, display his opposition against the "status quo" and its oppressive system, it is within character for Atticus to have such modus operandi, whereas for him to be vociferous is against character.
The whole point of the novel is to DO the right thing, and Atticus does just that. He makes sure that everyone in that courtroom knew the truth and his success, small though it is, is that the jury actually deliberated more than five minutes. His care in his respectful demeanor in the courtroom ensures that nothing he says or does is a distraction to the jury or the observers. It is revealed later that it was a Cunnigham relation that held up the jury. In the course of a few days Cunningham folk went from looking to lynch Tom to actually thinking about the situation. That is a small triumph. Things can't change overnight, but they do change.
I completely agree with above posts. Atticus's protest is in his fair, honorable, and caring defense of Tom Robinson. In a volatile setting such as the novel's Maycomb, a "protest" would have caused much more uproar than was already present. Had Atticus staged some sort of protest, his behavior would have gone against the advice he gives his children--which is to take the proverbial high road. He leads by example, and his example is one of equality, peace, and respect for others.
Protesting the system can be done in more ways than simply openly criticizing it. Railing against the wind is generally a futile undertaking. Atticus does more by agreeing to represent Tom Robinson, by giving him a good although futile defense, and by his own actions and treatment of the Black population of Maycomb tan he could have ever done by simply decrying the fairness of the trial in court. The way to change minds, the way to get people to listen, is through education. Atticus educates his children to not be racists, to look at people for who they are on the inside no matter the color of their skin, their age, their income level, or even their mental capacities. This is how the ext generation learns and how the next generation becomes more open minded than the one that came before it. Sadly, this is a slow process, and for Tom Robinson change did not come soon enough. But for every revolution, there are the martyrs, those who lost their lives as victims to the cause.
I would argue the opposite is true. In fact, Atticus does protest the system by his intention to actually give Tom Robinson a real defense. Because he believes in Tom's innocence, Atticus does more than just go through the motions and formalities of a trial--as was apparently the case for so many black defendants in that day and time. He treats Tom with respect and dignity, but he doesn't disrespect the white plaintiffs. Perhaps some would rather he had shouted down the Ewells or treated them with disdain to show the injustice; however, Atticus showed his respect for the people while pointing out the injustice to which his client had fallen victim. Atticus is also a state legislator, and while we hear next to nothing about his work there, his character is such that we know he's fighting for equality and against injustice in whatever ways he can.
I think that it would be unfair to criticize Atticus in this way. My reason for this is that protesting would not have made one bit of difference and would likely have just made things worse.
If Atticus protested, would the jury have changed their minds? Would they have said "oh, wait, we shouldn't be racist"? I highly doubt it. Instead, it would have given everyone a chance to focus on Atticus and say how bad he was. At the same time, the verdict would have been the same.
So I think Atticus handled it right. He did his best. He tried to get the jury to see past race. He hoped to get the verdict overturned on appeal. None of that would have been helped by him yelling about injustice.