Not all Japanese drink. Some East Asians have a metabolic condition that causes them to feel uncomfortable and turn red when they drink alcohol, so even though Japanese culture features a lot of drinking, not everyone drinks.

Other Japanese have had their doctors tell them to stop smoking and/or drinking. This is called dokutaa sutoppu "doctor stop" in Japanese English.

I have observed that when drink orders are taken in a group, there will usually be a group consensus to have a pitcher of beer or a flask of sake or whatever, but one person might say, "I'll have (insert name of non-alcoholic beverage)." No one questions it.

In my teaching days, I had students who had been Mormon missionaries, and obviously, they faced this situation on social occasions. They reported that bars always have Sprite or orange pop (known as juusu "juice") on hand for their teetotaling customers.

So there are many reasons why a Japanese person might not drink, and refusing and asking for something non-alcoholic would not be considered rude.