I'm just a geologist, not a wildlife expert...but here is my two cents worth.
Back in the 70s and 80s when the trans-alaska pipeline was being built many environmentalists where concerned that this would affect Caribou migration routes and birth rates.
What we have seen is that the pipeline was built high enough off the ground that it has no impact on migration routes. We have also seen the population of Caribou increase. The female Caribou are actually clustering around the pipeline to give birth. It is thought that this is because the oil flowing through the pipeline is warm, and thus creates a slightly less hostile environment for the calf to enter into.
These things in mind, I can see no reason why we should not drill in ANWR. Especially considering the advancements in directional drilling. This method makes it possible to access the oil in ANWR without actually having any above surface equipment in the area.