This is actually an inconsistent position. If there are really no objective moral truths, then there is no objective answer as to whether something should or should not be allowed. It is inconsistent to say that there are no objective facts that determine whether something ought to be done or not, and at the same time claim that abortion ought to be allowed, since to make the latter claim is to claim that something indeed ought to be allowed.
When this inconsistency is pointed out, some moral relativists might say that they are only affirming non-interference from their own perspective. But the problem is that from other perspectives, interference might not be undesirable and might even be necessary, and the relativist would then have no way to engage the other party in a rational discussion as to what the right thing to do is. For example, someone might think that abortion is wrong relative to his moral theory, and that all violent means are justified in order to prevent women from having abortions, including the killing of doctors and nurses who might participate in such matters. For a moral relativist, such a position is just as valid as thinking that abortion should be protected, and so no reason can be given to stop any such violent campaign against abortion. The obvious conclusion is that it would be a big mistake to think that moral relativism supports any kind of liberal moral outlook. Under relativism, any non-liberal or absurd position is just as valid as any other.
Contextualism urges us to be cautious with regard to moral claims. Is lying wrong? That depends on the situation. Lying to young children is sometimes of no big consequence. Is killing always wrong? Perhaps not when you have to kill somone attacking you out of self-defense. Generalizations about morality should take into account special situations. But being cautious about general moral claims is not the same thing as accepting moral relativism.
U05.4 Exercises
- If someone has committed a murder, then that person should be given a fair trial.
- Students should study hard and get a good grade.
- We should never toture any innocent babies just for fun and for no other reason.
What is written without effort is in general read without pleasure.

Samuel Johnson