There isn't overwhelming evidence, though. Native bird life in New Zealand has dramatically increased in recent years, despite cats continuing to enjoy relative freedom and huge numbers.
On the Dunedin study: >"A year-long study of 208 cats in urban Dunedin showed that they kill more birds, skinks, geckos, and weta than rats and mice."
>"37 Dunedin cats that were known to be prolific hunters, [...] without collars, the cats caught 378 animals, including 82 birds"
>"There is the well-documented case of a lighthouse-keeper’s cat causing the extinction of the Ste-phens Island wren. And near Tongariro National Park, one feral cat was filmed killing 102 short-tailed bats in the Rangataua forest, on the side of Mt Ruapehu, in just seven days in 2010."
https://www.forestandbird.org.nz/sites/default/files/2018-05...
https://zslpublications.onlinelibrary.wiley.com/doi/abs/10.1...
https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2486....
The success of native breeding, conservation, and re-introduction programmes has been in spite of the country's feral and domestic cats.
The lighthouse story is tragic and maddening. While I opted not to adopt a new cat when my last one died, I don't support the predator-free approach to conservation.
Why?
If hypothetically (since I'm not familiar with the data) they're killing some birds but those bird populations remain healthy, is that a problem?