I deal with this personally by arguing that artistic merit is effectively objective - that whether a work of art is "good" or "bad" is independent of personal tastes. There are lots of good works of art that I simply don't like (and frankly, lots of bad art that I love).

This is mostly as a counter to the common-as-dirt conceit of "I don't like this, therefore it sucks" that is many people's loud response to stuff that happens outside their own culture.