Shimshonit: Someone writes about having attended a shul with Filipino friends (gerei tzedek) and when the Filipino man sat down, a (white) woman came over and offered him a kippah. He pulled one out of his pocket and put it on, flustering her.
Not all Jews are white; they live all over the world and usually look like the people they live among. Ever been to Israel and seen a Libyan Jew? Or an Ethiopian? Or one of the Bnei Menashe?
In the situation where a woman handed a man of Filipino descent a kippah, it doesn’t necessarily mean she doesn’t think he’s Jewish, but the point is that he sat down in a sanctuary without a kippah. That’s not done anywhere I know of except perhaps a Reform synagogue, and perhaps not even then.
The most effective way to change things in Judaism is to do what has always been done: concentrate on making yourself a better Jew and person, be a participatory member of the community, and with your presence and persistence, slowly chip away at the establishment.
Good luck.

