The YouTube video linked below is an interview with a Ukrainian Shinto priestess, called Tatiana.
The video is all in Japanese, and while I looked at the autotranslate English subtitles, they are terrible. Nevertheless, they are, in most cases, better than nothing, if you assume that the really weird bits are translation problems. (Their conversation is entirely reasonable.)
Tatiana is a priestess, and licensed by Jinja Honchō. (I happen to know, independently, that this is true.) She may well be the first non-Japanese woman to be licensed as a Shinto priest by Jinja Honchō, although there have been a couple of earlier examples in other traditions. She is married to one of the priests at the jinja where she works, and that is why she was able to take the six-week training course that she talks about. She only qualified last year, and in the video she mentions thinking that, if the kami did not want her to be a priest, the course would be cancelled due to COVID, while if it went ahead, that was a sign that the kami was happy with it. (Obviously, it went ahead.)
Most of the conversation is about standard Shinto background, and thus things that regular readers of this blog already know. That includes the fact that non-Japanese people can become Shinto priests.
This is, however, another illustration of the real barrier to non-Japanese becoming Shinto priests: you need a strong connection to someone in the Shinto world who will recommend you. That’s probably harder to get than the necessary Japanese language proficiency. Marrying your connection is, however, definitely not necessary.