it depends upon a lot of factors.
first, it depends upon what the teachers is classifying as inversions. standing forward bend, downward dog--these are technically inversions, but most people don't think of them this way. those are generally safe for pregnancy.
likewise, certain back bends also are inversions--such as bridge pose and upward bow pose. these can be excellent for pregnancy, but they can also be risky depending upon the practitioner and her unique situation. so, most books and such might leave these out (or contraindicate them) simply because a small population of pregnant women might be at risk by doing them.
finally, more intensive inversions such as crow's pose (also called crane), hand stand, and head stand are commonly contraindicated, as are shoulderstand. the reason for this is really due to the experience of the practitioner (and also teacher in some cases), as opposed to whether or not it's "ok" for pregnancy in general. they are--but really only for experienced practitioners. most people coming to prenatal yoga are beginners, starting because they are pregnant. so, these sorts of inversions are generally avoided to keep these women safe from injuries that the postures could cause with the changed center of gravity and such, not because they would cause harm to the baby per se.
as ever in yoga, you are in charge. so while the teacher might encourage certain inversions, you needn't do them if you do not think or feel they are right for you.
personally, i did scorpion pose in the hand stand version and have photographs of it two weeks before the baby's birth (but around his EDD), so that's a pretty hefty inversion, back bend for being that full-on pregnant. but, i felt comfortable doing it, and so i did it.