What is a polite way to tell a person that I am only willing to talk to them if they do not operate a device which transmits my words to a third party in this way?
Keep in mind that being polite means you are respectful and considerate of others. You should therefore recognize that these devices provide significant benefits to some users, and that telling them to choose between you and their personal assistant may simply be impolite. There might not be a way for you to be respectful and considerate of your host when telling them that you'd rather not talk to them at all if they use such devices.
So if your goal is to be polite, then you should consider changing your question to one where the burden is placed on you rather than your host:
What is a polite way to find out if someone is operating a device which transmits my words to a third party?
A possible version might be something like:
I'm uncomfortable around personal assistant devices which respond to voice commands. Do you use any in this room/home?
After finding out the answer you can then decide how to act - the most respectful way would be simply to censor yourself and avoid saying anything you believe is too personal for such a device to hear. There's no need to point this out, unless you want to be tactless or blame them for your anxiety.
Thanks for letting me know.
They may respond by attempting to make you feel more comfortable, hopefully they will be good hosts, recognize your discomfort, and try to alleviate it.
If they do not, and you absolutely cannot speak in the presence of such a device you might instead indicate that you simply feel uncomfortable talking where one can hear you, and ask if there's a private place you can go without such devices, or request that your visit be moved to a park or restaurant - a more public place where perhaps you'll feel you have more privacy.
I see, thanks for letting me know. Unfortunately this makes me too uncomfortable to feel at ease. Is there another place we can visit together without them?
You could ask that they be disabled, but that involves 1) cutting your host off from their personal assistant (and perhaps their home automation system) and 2) requiring the host to figure out what you mean (is mute enough, or you you demand they be disconnected and unpowered?) and then go around and do it, then undo it when you leave.
I'm still very uneasy about them, I hope you understand, but I just can't talk when they are on. Would it be too much trouble to mute/disable/disconnect them while I'm here?
Again, this is definitely outside respectful and considerate territory - once you made your discomfort clear as in the first two statements, they should respond, or you should simply make an excuse and leave. That said, an argument could be made that they, choosing not to respond in the manner you'd prefer, have shown you disrespect and so continuing down this path might be acceptable depending on your level of tact and your relationship with them.
If they are good friends they will probably acquiesce without further issue, but given that they've chosen to live with these devices it would continue to be a burden every time you visited, and you would have to weigh the value of that relationship against the burden you are placing on it. Keep in mind that while you may see it as your personal space being invaded, this is their home and they may see it as paranoia that they have to put up with if they want to maintain your friendship.
Given that these devices don't transmit unless the wake word is used, you probably shouldn't weigh your anxiety so heavily in the balance.