Or at least, things claiming to be hand sanitizer. Which just makes the rule more absurd. If you've got a favorite shampoo, time to go looking for a nice large hand sanitizer bottle to transfer it to. (Though I wouldn't do that for contact lens saline, a thing I'd kinda like to bring on in large bottles, since the small ones are absurdly expensive and somewhat less available.)
They technically allow large bottles of contact solution in carry-on because it's a medical necessity (https://www.tsa.gov/travel/security-screening/whatcanibring/...). I just keep it in my toiletries bag and they pull it out to run a quick test most of the time.
I've had a bottle of hand sanitizer in my bag for years and they've never once said anything. Either their security is so bad they've never caught it, or they've always been lax about sanitizer.