Separating the 'artist from the art' is almost always hugely misinterpreted, and it often doesn't mean 'pretend the artist doesn't matter so I can keep enjoying their content.' Ultimately you have to decide for yourself what you will or won't accept, and that will be down to your personal ethics or values, and how you express those ethics or values.

If my favourite fanfic author was suddenly revealed to be a TERF (unlikely as they're trans, but y'know, it could happen), I personally couldn't enjoy their writing anymore. I wouldn't be able to escape into their stories or characters, knowing the person who wrote this thing I love doesn't believe in my right to exist as I am, and wants to constantly debate my human rights. I can't suspend my disbelief that much.

But then, on the other hand, I can still watch the films of Harvey Weinstein, a horrible fucking human being and scum on earth, and justify this by knowing that many of the people who made that film are not horrible fucking human beings and he is not the only person to consider. Some people would disagree with my choice. Others will understand.

That's me, but everyone is different on matters like that, and so then it comes down to how you show support. If you continue to read this author but never give them a platform, never like their fic, comment on the chapters, interact with them in any way, rec it to another person (not without 'you should also know they're a rabid transphobe'), be a 'silent consumer' etc. and consider this the way that you demonstrate that you don't support this person's beliefs/views, that's also valid. You still express your values by lending nothing to this person that they can then benefit from. This is how some trans people still consume the works of JKR - making sure she never sees a single cent or benefit under the proud flag of piracy - for example. There are going to be other trans people who disapprove of this, or don't like this, who even make good arguments against it, and tbh, I'm on the fence about it myself, I can just understand why people come to this place with it.

Some of those expressions of our values can be problematic - paying for the work of someone who is transphobic (which you're obviously not doing in the case of fic) directly benefits a transphobe who is publicly transphobic. That's just...straight up harmful. That doesn't really express your values. In fact it may express opposite values. Reccing the fics of this author for example, knowing other trans readers might find the side blog one day and feel deeply wounded and betrayed, expresses opposite values - this would be problematic.

You might be someone who sends them a message anonymously or similar, to let them know that their views are hurtful/hateful and ask how they feel knowing that trans people are reading their stories, and see if they respond to you. Maybe they've never thought about it before. But you don't owe them that kind of labour. You may also want to consider naming/shaming them, to at least do fellow folks in your community the courtesy of avoiding a transphobe. The fact that you've gone out of your way to protect their identity even in this anon, is not something you owe them.

There are going to be different ways you make peace with this situation anon, and don't be surprised if they change over time, depending on how you feel about it. People can only tell you what they would do based on their values, and you must sit down with your own values and decide which actions support your values, and which go against them. We don't all express these things in exactly the same way. As long as you're not expressing harmful or opposite values, you're generally going to be okay, and there is sometimes room in that to still enjoy the fic, if that is something you're able to do.

(Please see the tags since I address this in a bit more detail - although the tl;dr there is - have you considered that instead of continuing to be entertained by the works of a transphobe, maybe if you stopped reading them, you'd find someone you liked just as much, if not more, who will replace them? Sometimes the harm we do is simply in giving our time and energy to someone who wishes we didn't exist, and is actively protesting against our existence - when we could look for others to entertain us who don't expect horrible ethical quandaries from us just to enjoy what they're creating).