As a native British English speaker, I believe "on society" feels better than "in society".
"Society" is the thing being directly affected here, by a commercial / scientific practice which at this level is independent of "society".
"Society" may be considered as the structure which is the aggregate of the net effect of interactions between the people in it.
On the one hand, animal experiments may result in the development of medicines or the improvement of safety of products used, which benefit "society" because people are healthier and happier, and society is "improved" as a result.
On the other hand, a casual disregard for the rights of animals and their welfare can lead to a more casual disregard for the rights of humans, and even lead to an erosion of personal freedoms and comfort at the expense of those who don't see anything wrong with exploiting others for their ends.
The effect is "on" rather than "in" here.