We can't. We never could, and never will. Art is inextricable from the context that created it, which includes the artist(s), the time, the place, the culture and acquaintances and ideas that are all woven into the fabric of the work.

When we say "separate the art from the artist" we mean we elect to ignore a part of the art that makes us uncomfortable, but ignoring a thing neither makes it not so nor prevents it from influencing us. Art has ideas and subideas the same way a musical note has overtones, but on a million different ontological dimensions. The artist is only aware of some of these; the others are assumptions, biases, cultural and personal blindnesses, prejudices, coincidences, and bursts of artistic genius.

Side note: you don't have a one-way relationship with art. If you think you can experience art without that art changing you in some way, you are merely blind to its influence. Art changes you. Not always in big ways, and not always for the better. Your options are to either acknowledge and explore the nature of that change, or not. Even refusing to engage with a work of art is an acknowledgement of that work's influence on you.

Back to the main note: even though it's impossible to really separate art from its context (like where it came from), ignoring the context does flatten the appearance of the art and make some of the ideological overtones of the art invisible. We do this for all kinds of reasons: art as unchallenging entertainment is easier to consume passively, so ignoring the challenging parts of it feels good. Like enjoying the rhythm and melody of a pop song without dealing with the misogynistic lyrics, or the political affiliations of the artists. Thinking about those things is hard. Not thinking about them is easy, and it gets easier with practice. Practice ignoring the uncomfortable parts of art long enough and it becomes habitual. Eventually you ignore them without even thinking about them.

They don't stop affecting you, though. Those overtones seep into your brain and influence your thinking in ways you will never be aware of, because you have lost the ability to detect them. It happens gradually. After ten thousand subliminal messages, you'll hold beliefs you neither understand nor can even fully articulate, and you won't know how to change them. It's possible, but it takes almost as long to undo as it takes to do, because they're hard to find.

Second side note: Propagandists are well aware of this property of art, which is why propaganda works, more or less, even when the audience "knows" its propaganda. It's a quantity over quality thing: the overtones slip though unobserved even if you are aware of the main gist of the piece.

That's why you don't separate the art from the artist. You can't, and pretending to do so denies what art does, much to your detriment.