The term "design" is ambiguous here.
When design is a process to build something pleasing (like in music or painting), then yes, it's an art, and you can rightfully have different opinions about outcomes, sometimes diametrically opposed opinions, which is all not just fine and accepted but inherent in the field and a required ingredient.
When design is about building something functional, then it's part of engineering. You can objectively measure whether it does satisfy the requirements. That's where serious engineering disciplines are and where software engineering needs to aim for if it wants to keep engineering in its title without getting laughed at. As long as programmers consider themselves part artists, that's hard to achieve, but as the field matures, there is hope.
Note that some fields are trying to be both. For example architecture. There it's solved by making a more or less clear distinction between the pleasing art part (that's what the architect does) and the functional engineering part (structural engineer). Both roles are not being conflated. In software, we still do that.