I only have a passing familiarity with the SCA but I saw your recent ask and I wanted to ask is it not considered yellowface for a white person to have a Japanese persona? If a white person having a 15th century African persona wouldn't be ok (which I hope is the case) why is Asian ok? I know Japanese people are generally very happy to share their culture and clothes, but a white person who doesn't even speak Japanese regularly roleplaying as an Asian seems difficult to be done respectfully.
I really appreciate you asking this, and I'm going to try to answer you in a way that I hope is helpful and respectful. Since your question is on the persona, I will focus on that. If I say anything wrong or misleading, I hope others will correct me.
I think the keyword in your question is 'roleplay.' To clarify, the SCA is not a LARP, it is living history. You will hear a lot of talk about "the game" in the SCA, but it is, in actuality, a non-profit educational organization. Members research and recreate the arts and sciences of the middle ages, sometimes with the help of a persona.
A persona in the Society is used by many members to give focus on a certain time and place that interests a person. Sometimes a persona is simply a time and place to base your fashion or kit on, but other times it's to better understand and educate yourself and others on different people and places. For those who are interested, it gives them a definitive focus to research the role someone would have played in society, their skills, their profession, as well as their culture. This isn't pretending to be a race that you aren't, this is educating yourself and teaching others about the historical and cultural importance of other times and places and the people who existed there.
It's also important to remember that people of color traveled as extensively as their white counterparts. Black, brown, and asian people existed in medieval Europe, just as white people existed in medieval Africa and Asia. The idea that you should only use a persona that shares your race is a fallacy, because medieval history is world history. There were brown people who are culturally German, and black people who are culturally Chinese a thousand years ago just like today. Learning about and appreciating how people existed in times and places different than our own is a beautiful and important part of the SCA.
A household sister of mine is black and has a Japanese persona. She has the most stunning garb I've ever seen and loves to explain it all in detail. A Filipino friend has a Moorish persona and is an absolute encyclopedia of information about all things Al-Andalus. A white friend has a Korean persona and routinely gives a classes on the cultural importance of tea ceremonies. Each of them is a font of information about different historical and cultural importance and contributions of their time and place, and I'm grateful for their taking the time to learn and teach about it. Which is exactly what a persona is meant to do.