Should I let my child drink root beer?
Sure. Why not. It's just a beverage (carbonated sugar water).
Frankly, I'm more surprised that you have a child than you fretting about allowing the child to drink root beer. Here in the States we have a funny diaper commercial. It shows the mother fretting about all sorts of details about her kid. She interviews like dozens of babysitters. She selects organic, fair trade this-or-that. She is super idealistic. Then they show her with the second kid and she's all, "Oh who gives a f–k. Kids are resilient."
Parenting — so I'm told — shatters idealism in rearing children because fairly quickly, parents realize that they're not programming robots. They're parenting human beings. Those human beings aren't receptacles for rivers of idealism, but who almost always come at the world with their own views and desires. This has to be true of your kid.
I'mma' tell you a secret. No matter what you do to your kid, that youngin' is gonna have sex before they graduate school. Your kid is gonna' drink alcohol. It's highly likely that your kid will try drugs. It's almost a certainty that your kid will lie to you with impunity and probably steal a few things in their lifetime. Get over it. This doesn't mean you don't correct, admonish and otherwise engage your kid to turn them into a proper human being. But fretting over the minutia is going to be a huge waste of time.
Fairly quickly, parents realize that they're not programming robots. They're parenting human beings.
When I was a manager, there was a saying, "Major in the majors." Basically this, "Find the shit that matters and make that your focus. Doesn't mean that you ignore the little things, but that you deal with the stuff that is really important. If you fight every tiny battle, you'll have no credibility or energy left when the big stuff happens."
Go ahead. Freak out about root beer. Have at it. Just remember, you teach people how to respect you. If you're going to fret about nonsense like root beer, I promise you, you'll have nothing left for the really important stuff like when your son comes home stoned or your daughter tells you she wants to go on the pill.