To those wondering "Why are you posting things about how you're coping with your ageing parents?"

Because not everyone has a good relationship with their parents and not everyone that has a strained relationship knows what options are available to them for dealing with it in a healthy and sane manner.

I don't claim to be the paragon of mental health, but I spent a LOT of money on therapy and worked very hard and I love giving that away for free.

The baseline is this:
1) It's okay to put your health, mental and physical, first. In fact, it's necessary.
2) You are under no obligation to respond to their outdated ideas. (Because there is no audience in text messages, I just ignore my stepmother's anti-immigrant rhetoric because she will not change and I am here to discuss my father's health, not her political paranoia.)
3) They will try to push your buttons. Take a breath and go into customer service mode (but as that manager you liked). "Yes, I hear your concern. I understand that you're upset. Here are the limitations of physics that we're dealing with and I can only work within the actual universe we reside."

And finally...

You are free to walk away at any time. You may have to in order to protect yourself. It does not mean that you have failed. It means that you have succeeded in doing what they did not: protecting you.