I personally dealt with that... here's my story:
On the way to China, via Moscow, so dealing with Italian and Russian airlines, no issues. I had my 50ml bottle of hand sanitizer and they didn't even blink at it.
On the way out, leaving from Beijing, it was a big NO for the same bottle. Basically, if it has a flammable sign, it's not allowed on board, no matter how much you argue with them. Same thing happened with a travel-size deodorant spray that i travelled with multiple times through Beijing/Shanghai and was confiscated when i went through Luoyang.
so, your mileage will vary but the rule of thumb is avoid anything with flammable signs or find a way to remove/cover them.
Many of the small size sanitizers sold now don't have it. try and get those.