Shinto is a religion and that is a fact. Worshiping a Shinto altar (Kamidana), is worshiping "other gods". Over a 100 million Japanese observe Shinto events (e.g. New Years, Shogatsu) and visit their local shrines.
Christians, Muslims, etc, that bow to a Kamidana have some serious soul searching to do...
Most of the Japanese people I met described their role in attending Shinto events as non-religious
Yes, worshipping the altar, would not be worshiping "God." However, a distinction can be made (and is up to the individual to adopt or not) between bowing and worshiping. If one can bow to their king (who is not God) and be said to not be worshiping said king, why not kamiza?
So for some, bowing to shomen where kamiza or shinza are, is just
showing respect for the tradition.