Acceptance is not approval. But we often get them confused. People often assume that acceptance means approval, but they are two different things not necessarily related. As Buddhists, we accept things as they are, but this does not mean we necessarily approve of things as they are. Sometimes acceptance and approval go together, and sometimes not. So I think it is good to be aware (accept) on one channel, while recognizing that on the other channel you can have your choice of approval or disapproval. An example: I accept all the suffering in the world, but I don't approve of it. Another, more explicit, example: I accept that John Doe beats his wife, but I don't approve of it.
The way I see it is that acceptance is openness and awareness; it is pre-judgment of approval or disapproval, which are labels, which are secondary to whatever it is we are accepting (being aware of). By starting with acceptance as a base of action I am able to operate in the world more compassionately, but if I start with approval or disapproval the self gets in the way and things get rougher. Using the John Doe example, if I start with just accepting that he beats his wife instead of immediate disapproval, then I am more likely to try and help him, and because of that he is more likely to work with me, thus creating a more positive karma for all. But if I start with disapproval, I am more likely to act in a negative manner and John is not going to work with me. He might get pissed off and then take it out on me and his wife, thus creating a more negative karma for all. (Please, this is just an illustrative example meant to dramatize the issue. If it upsets you or you feel it is a poor one, I apologize and ask that you accept it instead of disapprove of it).
My point here is that typically, our approval/disapproval channel gets really good reception, but we need to put our antennae up higher so that we get better reception of the acceptance channel. And, most importantly, (1) recognize the difference between acceptance and approval, and (2) act more from a position of acceptance instead of approval/disapproval.