Alcohol rubs aren't enough
Those who use alcohol gel sanitizers know that their skin gets dry and cracked. Everyone I know has to use hand lotion constantly. The alcohol can do a great job of getting your hands clean (see citation below) but is also good about putting a strain on the health of your skin.
And here's the relevant paragraph from the article:
Your hands are one of the main routes that viruses make their way from surfaces to your respiratory system, so keeping them clean is one of the most effective things you can do to stop yourself contracting the virus. Wash your hands thoroughly with soap and water where possible and if you can’t get to a sink, an alcohol-based hand sanitiser will do the trick.
And there are other problems with alcohol based hand rubs (ABHR) including these, and these, and this. Basically, ABHR aren't used in enough quantity to cover your entire hands, they aren't on long enough to ensure sufficient sanitation, and alcohol doesn't do as good a job at sanitizing as soap.
Also you can search for the CDC Hand Sanitizer Factsheet,
and this source tells you that hand washing is at least as important as alcohol rubs:
So don't be afraid to use Earl's as much as you want to get clean and healthy at the same time. It's just as good at being "anti-bacterial" and "anti-viral" as anything else on the market.