Is it Yuck? Yes of course. But it also seems extremely unlikely. And it's a lot less Yuck than thinking about what's in the sand in public playgrounds that all kids visit constantly. And while I have a reasonable chance of preventing them from licking the seats, I have no chance of preventing them from eating some sand.
This is just a bizarre irrational worry...
Do you and your kids take public transport regularly? In a failing city/society, that is.
Because if the answer is "yes, I do take public transport in a city that struggles to pay its bills and I still don't care that the chairs have weird organic substances on them" then fair-play to you, but for me personally at some point I had to purchase a personal car (when I was already approaching my mid-30s) because I just couldn't convince myself anymore that it is ok to not want to sit down inside of a train ("better stand up by the window, that seat is too dirty").
And these robo-taxis will be worse than public transport, for the main reason that there's no-one "standing guard" inside of them (and, no, Big Brother cameras placed inside of them, which should be a dedicated topic all by itself, btw, really won't change a thing in that respect).
If you soil a waymo taxi, they can ban you from ever booking another one, the same cannot be said for public transport
While I consider this somewhat dystopian, I do think it's pretty clear that they will be much cleaner than public transport for that reason
You reached a situation where everyday things are "too dirty" and rather than realising that's a mental health problem and you might need to fix that, you... found an expensive and elaborate coping strategy which necessitates further crazy beliefs.
Do you avoid handrails and sanitize the doorknobs and gas pumps you interact with? Those are going to be far worse than subway chairs. It's probably not a bad idea, but it's a bit beyond what I suspect most people consider normal. I had a friend who lived like that, and he ended up being diagnosed with OCD.