That is to say it will definitely affect flavor, but how it affects the flavor is ultimately dependent upon the specific mineral compounds found in your hard water vs. other hard waters and soft water's lack of these compounds.
Here's the key: Some of the compounds in hard water are "sticky," glomming onto certain compounds in coffee when they meet (in your coffeemaker). The more eugenol the water hangs on to, for example, the woodsier the taste of your coffee will be.
Magnesium is particularly sticky, meaning water that's high in magnesium will make coffee with a stronger flavor (and higher levels of caffeine). Hard water can also have high levels of bicarbonate, though, which Hendon found could lead to more bitter flavors coming through. - A Chemist Has Uncovered A Secret To Brewing Delicious Coffee At Home Business Insider.
So depending on flavor preferences you might prefer your hard water at home but dislike it at work or simply prefer soft water altogether. Traditionally hard water is actually sought after for other beverage processes like beer brewing because of some of the abilities described above.