There's a general exemption for personal care products. Has to be a small bottle and in a clear Ziploc bag or equivalent. (Rarely enforced, in my experience)
I been barked at many times for water bottles standing in line—usually before the liquid dump station, which makes it even more grating.
On the other hand, I've accidentally left large bottles of contact solution in my bags more than once (when I expected to check a bag but ended up doing carryon, and forgot to repack the liquids), and never been stopped for it. 100% security theater
https://www.tsa.gov/travel/security-screening/liquids-rule