It doesn't cheapen the word. If discrimination is intentional and has the effect of minimizing and eventually eliminating the target ethnic group, then you have the same result as if you lined up everyone in that group and shot them.

The word is attached to the intended outcome, not the specific actions taken to achieve it.

Of course it cheapens it.

Using your example, if some ethnic group changed how they dressed it would be genocide.

That cheapens the word. Change in dress is not as severe an outcome as buried in a ditch with a bullet in your head.