Separating the art from the artist is usually meant for academic settings when discussing works from people who were flawed (I’m using very mild language) or who we see through a modern lens as problematic. It’s how we can talk about the themes and IP that Lovecraft created despite him being a truly garbage human being in his life.

I think we have collectively co-opted the phrase to try and engage with entertainment we like when the artist is problematic. I think that’s generally okay if the artist is no longer alive or does not own the IP anymore.

If an artist is alive and actively a shitty person, then it’s not really possible to separate their art from them in my opinion (again, non-academically). Doing so can give money, clout, or other forms of power to further enable them. That’s why we’ve been seeing “cancel culture” grow, because boycotting is one of the few ways to limit an artist’s reach if they are using their art or status to hurt people.

As an aside, depending on the artist’s actions or reputation, it is genuinely seen as suspect to engage with their art outside of academia even if they are dead. This can be especially true if the art itself espouses dangerous or very hurtful ideas. A common example is stuff like Mein Kampf, which has been studied academically/historically in order to understand it. I think anyone would be wary of someone saying they are a fan of it though.