This is a question of relativism. Taste is ultimately about value, and "good taste" in art is just one aspect of culture at large. So, if you doubt if "good taste" exists, you also probably think that everyone has the right to believe whatever they want and everyone should be able to exist how they want. You can call this relativistic individualism.

I bring this up because the topic reminds me of a philosopher of religion, Charles Taylor. One of his points is that this relativistic individualism inevitably leads to our own inability to express what we value. It's a kind of "explanatory atrophy." If your default position is I have my way and he has his, and that's all there really is to it you lose the ability to present and shape your own opinion in reaction to others. Most people don't have the vocabulary to articulate this, so "that's in bad taste" ends up just turning into Dudeism.. that's just your opinion, man.

So when confronted with something we think is in bad taste, we can't put vague thoughts into words, and therefore just fall back to "it's his/her personal taste, who I am to criticize?"

Ultimately, this question arises from a lack of education and cultural interest in the arts and in aesthetics. Without it, the definition of good taste will ultimately boil down to the opinions of whoever has money, power, or popularity.