Is being too cautious a thing when driving?

I am still learning how to drive, I have the basics of driving down but I'm told I should be following all rules of the road no matter what happened previously.

An example of this is when I was going 27 in a 30 because there tends to be cars that don't stop at the stop sign of the intersection and just keep speeding through, and while the cars behind me have no problem (they don't honk or speed around me), the people in the car with me tend to tell me I'm not going to get my license if I'm not going the speed limit. Or if I'm waiting at a stoplight, going to turn (because that is legal in my state if there is no oncoming traffic in the lane that isn't crossing over), how I should just turn because the people behind me are impatient and it's making my passenger nervous but I don't see a safe opening.

I simply just don't want to risk putting myself or others in danger just because I cannot find a safe spot to merge into traffic when we're running late. And I'm worried that when I go to test for my license that me being cautious and explaining my thinking to examiner means that I probably shouldn't be driving on the roads. Even though everyone around me never drives safely because everyone seems to want to go the legal 5 over.

Is it wrong to do things like that when you're unsure of the circumstances but want to keep the people in your car safe? Or should I just be following the road rules and ignoring being as cautious?