Vinegar is ok in small doses.
It's ok for the straps to get damp. And most times a kid vomits the straps don't get soaked, they get damp. If you wanted to use a dime sized dollop of gentle soap on a wet washcloth and did that over the entire strap, that'd be considered, IMO, spot cleaning. Putting them through a washing machine with an agitator and a bunch of soap can do damage.
Most times if the harness is SO absolutely soaked from vomit you're not going to be able to clean them without putting them int he wash anyway, and you'll likely replace them just because they stink to holy heck. So it's likely the stomach acid can hurt them, but in the amount it would take for enough stomach acid to saturate the harnesses you'd toss them anyway.
Whenever Piper threw up big time in the car (she's not a vomiter, but she was Mt. Vesuvius as a baby) if she was throwing up so so much in one go it'd go far. I had to be more worried about the backseat rather than her harness. It was the smaller amounts that ended up on her harness. And they got wiped down immediately. And if it was a lot and she was going to keep vomiting, I'd already pulled over after the first and was holding her out of her seat to finish the rest of it. So a stomach full of acid, completely undiluted, I think is rarer than you think.
Wendy