Thank you for writing this, Molly. No, seriously. As an East Asian woman, thank you.
I know many, many white woman are a relatively well-educated, progressive set of people who stand for the improvement of minority rights, but these same women may not see that the paranoia behaviour they exhibit is, in a very subtle way, kind of offensive. The “me first!” attitude you mentioned is a perfect way of describing it.
If you’re a white woman who is a feminist, an advocate for justice, compassionate…please think a step deeper about how your actions can be construed from the outside. If you really want to help, be calm, wash your hands, practice good hygiene, and maybe educate your white male friends (I’m saying white male friends because this demographic still has the most power in the western world!) to please do so as well and don’t automatically assume all Asian people are somehow more likely to carry the virus.