Brutus loves Rome and believes in the republic. Would he be betraying his ideals by aligning himself with Cassius?
In a sense, Brutus is aligning himself with what Caesar describes as a man who is dangerous...
Yon Cassius has a lean and hungry look. / He thinks too much. Such men are dangerous(1.2.193-196).
This is Caesar's summation of Cassius.
Either Caesar was guilty or Cassius was power hungry. For Brutus to align himself with a conspiracy is a necessary part of keeping Rome an ideal republic. Whether or not Cassius is the ideal conspirator is another story.
Bloodshed is an inevitable part of life. When dictators try and change an ideal republic to a dictatorship, something drastic has to be done to keep the republic ideal. Brutus did what he had to do. Whether or Cassius is an ideal conspirator is all together questionable. Perhaps, he did have a "lean and hungry look." Perhaps, Caesar was expressing his concerns based on his guilt of becoming overly ambitious.
Brutus aligned himself with Cassius because Caesar had become overly ambitious. Whether Cassius gets credit for persuading Brutus to join his cause is another story. Would Brutus have eventually felt compelled to rid Rome of a dictatorship?
Brutus is an honorable man. He did not need Cassius to point out things he was already sensing. Cassius just happened to be the first in line.
No, he's not betraying his ideals because one needs to identify Brutus' motives and intentions in aligning with Cassius. Brutus didn't realize how manipulative and vengeful Cassius was. He believed Cassius did care about Rome first and foremost. Brutus is an idealist and he wrongfully believes the other conspirators are too. So in order to betray his ideals, he would have had to know the true intentions of the conspirators. Brutus' intentions were always noble; unfortunately, he was taken advantage of by some less than savory characters.
The question at hand here directly points to the methods Cassius employs to convince Brutus to join the conspiracy.
It is because Cassius has framed the conspiracy as one seeking to defend Rome from tyranny and to help Rome maintain its form of government that Brutus can agree to join the conspiracy with his principles intact.