Why was it important for Romans to present themselves as fundamentally traditional even as they embarked on potentially revolutionary actions?
I assume that this question refers mainly to the actions of Romans in the time of the Roman Empire (as opposed to the Roman Republic). During this time, emperors (starting with Augustus) often tried to portray themselves as maintaining traditions when they were actually acting in relatively revolutionary ways. The main reason why they did this was because tradition was so important to the Roman sense of who they were and what their government was supposed to be like.
Rome did not have a written constitution that said how its rulers were supposed to act or how its government was supposed to be set up. Therefore, the legitimacy of Roman emperors could not come from written law. The emperors had to find some other way to show that they were the legitimate rulers of Rome and that they should be respected and obeyed. One way to do this was to show that they were following tradition. In this way they could show that they had the right to rule because they were simply continuing on in the way things had always been done.
This was particularly important given what had happened to Julius Caesar. Caesar was well-loved by many, but he also scared people because he did not seem to be trying to maintain tradition. His actions were so untraditional that people could credibly claim that he was trying to set himself up as king. Because of this, he ended up getting assassinated.
Roman emperors wanted to show that they were legitimate so that they would be able to rule effectively and so they would not attract opposition in the way the Julius Caesar did. In order to do that, they tried to convince the people that they were really following tradition. That way, they could get away with doing things that were very much non-traditional.