The rebuttal I've heard to this is that they're not killing the same birds. Cats kill small, common birds like robins and sparrows whose populations can easily absorb the loss. Wind turbines kill larger, rarer birds like eagles and owls, whose deaths have a much bigger ecological impact.

Someone more qualified than me can dissect this argument and crunch the data. Just mentioning it to illustrate that the "they kill birds!" argument might be more nuanced than you think.