Third trimester? Not acceptable, except to save the life of the mother.
First trimester? Acceptable IF the mother desires it, but only the mother has the right to decide. She cannot be forced to have the abortion, nor can she be forced to carry the fetus against her will.
Second trimester? Here's the real problem. This is the foggy area where most pro-abortion people, I think, run aground. This is where, IMO, the question of "humanness" comes into play. I don't know where the dividing line is, but if there is one, it's in this time frame.
There is a point in the development of the fetus where extraordinary medical intervention can save the baby if it is delivered prematurely. There is another point where the child can survive with no or minimal intervention. Somewhere between these two points has to be the demarcation.
But regardless, I don't feel it's the government's business to determine whether or not a woman can abort her fetus. That has to be her own choice, and her own conscience must guide her.