The ecological impact of a few cats is tiny compared to that of a human. If you really care about the environment, don't have children and maybe kill yourself too
On avian populations, that simply isn't true.
"According to their calculations, outdoor cats killed somewhere in the ballpark of 2.4 billion birds and 12.3 billion small mammals in the U.S. per year—far exceeding any other human-influenced cause of avian death, such as pesticides or collisions with window."[1]
I agree with your concerns regarding human overpopulation though. My wife and I aren't having kids.
[1] https://www.smithsonianmag.com/science-nature/moral-cost-of-...