I have a hard time with this one. If compassion means that you truly care about others, you might feel bad for people that are doing something you think is wrong but then you are still going to think it is wrong. You can feel compassion for them and want to help them as much as possible, but it shouldn't change your moral conviction in the sense that you would suddenly excuse any behavior because you are afraid to get someone hurt or hurt them. Sometimes people need to be hurt or need to be told that what they are doing is wrong, but that might not seem "compassionate" in the more popular vision of the word.
There is a difference between treating people "as if" we care about them and truly caring about them. Morality is making what is considered to be the right choice. Right choices are sometimes made because they are simply the right choice. I would say that it is more of a moral choice when we make the right choice regardless of whatever personal feelings we have.
If you define compassion as caring about others, then I do believe it is the basis of all good moral systems. For example, Kant says that we must always treat others as if they are ends in themselves -- not just means to our own ends. This, to me, is an example of compassion because we are treating people as if we care about them.
I think it's important to realize that compassion and license are not the same thing. For example, you wouldn't want to let someone steal with impunity because they have a hard life and you feel sorry for them. This is, in the long run, not compassionate because it does not help them improve themselves. So compassion can, at times, take the form of "tough love."