Considering that Pontius Pilate (the Judean Prefect in the Roman Empire) awarded death by crucifixion to Jesus just for calling himself "King of the Jews", I don't think they held much rights. Or else, the rights were there just as a farce, but could be crushed easily by powerful people in the society at their will.
However, in case of Jesus, why even make the farce of a courtroom trial, what was stopping the state from just kidnapping Jesus overnight and kill him discreetly?
But there was also the case of Israel/Judea not being a proper Roman territory, but a place where they had to share powers with the local Jewish overlords there, I guess. So, don't know how big of a role that played in the trial of Jesus. Maybe, if Jesus was a citizen of an integral Roman region like France or Italy, he could have been perhaps spared?
Christ was not a Roman citizen, and therefore not subject to Roman law. Instead, Christ was a provincial, subject to the ius gentium and to his local peoples' laws. Thus Pilate makes an appeal to the locals and is able to crucify him in the first place, a punishment from which normally Roman citizens were exempt (although by later antiquity the legal class of humiliores could technically be crucified). Likewise, Paul, an actual Roman citizen, in the famous passage in Acts protests his manhandling by noting his status as a Roman citizen, which should by rights exempt him from physical mistreatment. Theoretically Roman citizenship, which was quite rare in the provinces c.30 AD, entitled its holder to certain important benefits. Apart from connubium, the right to marry according to Roman law, suffragium, the right to buy and sell res mancipi (e.g. Italian land), the right to run for office, exemption from tribute (but not the vectigal), and other such privileges Roman citizenship also exempted individuals from punishment by scourging and crucifixion (via the lex Porcia), guaranteed the right of provocatio, and prevented the execution of the citizen without trial (via the lex Sempronia). Had Christ been a Roman citizen then theoretically he could not have been punished thus (and the input of the locals would not have been sought). But at the same time, the law could be broken, and appeals to Roman citizenship were not always clear. Christ at no point in the gospels claims to hold Roman citizenship.