"But what am I supposed to do about it? I'm not responsible for racism; I'm just talking about how I feel!"
Indeed, it can feel unfair to be accused of racist beliefs when you're just trying to express yourself. Your frustrations are understandable. But do remember that it's much, much worse for people of colour to be subjected to constant reminders that others don't notice their pain, or care about reducing it.
The number one thing is to do your research. Look into the thing you are and get accurate information about it (not just from Tumblr) before deciding you are it. If you fit a visual image such as skull-deer or many-tailed fox, but you don't resonate with the actual legend you are drawing on, try describing yourself as just "skull-deer" or "many-tailed fox". It'll be more helpful to you, too, to not try to squish yourself into an image that doesn't really fit.
(I could describe myself as an "Eastern dragon", and have in the past: I'm wingless, associated with water rather than fire, and aspire to be a benevolent force and a guardian of nature. But I'm also white and my dragon form has strong connections to European regions and myths, so I feel it's better to describe myself as a wingless dragon or drake. And acknowledging that allows me to connect more authentically with my Slavic heritage, as a half-Pole.)
The second thing is to be respectful, humble and open to correction. It's easy to say, "well, I didn't mean to do harm, so you shouldn't be mad at me!" But do you think that's going to make anyone feel less hurt? Would it make you feel less hurt if someone said it to you? If someone says a thing you're saying is racist, take the time to listen to them without getting defensive. Accept that you have hurt them, even if unwillingly, and be open to their suggestions of how you could express things better.
The third thing is to point out racism when you see it in the community. That doesn't mean making callout posts or sending hate, but just calmly stating why the thing they said is an issue. e.g. "I'm not criticising you personally, but be aware that X myth has roots in white supremacy." Or, "this creature represents Algonquin stories about the dangers of greed and selfishness and how it can turn you into a monster. Are you actually saying that you embody that myth, or are you saying that you relate to modern depictions of the creature? If the latter, it's kinder to call yourself a skull-deer or such."
When white people stay silent on these matters, we allow racism to spread unchecked. It's uncomfortable to stand up against racism and draw attention to yourself, but to the people constantly being bombarded by hurtful narratives, it could mean everything.