I'm not sure what you think your threat model is here. I'm not happy about it either, but my place of residence isn't entirely private information already. I'm pretty certain it's available through multiple public information sources. Cameras being able to see me in that vicinity might help someone determine my daily habits and schedule, but there are many other ways of that as well.

Again, I'm not happy about it, but I feel like you need to ask yourself what risk you're trying to protect yourself against here.

As another commenter pointed out, any of the amazon based ones are part of amazon sidewalk and record nearby bluetooth and wifi devices. Sidewalk is also partnering with flock, so that data is available to law enforcement and possibly corporations that use flock for security to be able to use for advertisement.

But so is your phone's location data.

So if you're trying to protect against this sort of thing, you'd need to be taking much more extreme steps. Different dogs at different times with entirely different outfits and rocks in shoes to make different gaits. Face coverings. Multiple burner phones not tied to your identity, and only taken out of farady bags to use in association with different identities.

And then it still would all tie back to the same house/general vicinity.

There's no perfect privacy options, so you need to identify your threat model. What are you trying to protect against, how important is it, what are the quantifiable risks of failure, and how inconvenienced are you willing to be to achieve this.

It sucks. I'm not happy about it. But you can't stop your neighbors from using them. So you'll need to accept it, or come up with alternatives. Feel like moving to someplace more rural?

It's always going to be a balance.