oomis: There’s a serious machlokes about that. Both my rebbeim told me it’s not a problem but others disagree.
Today I saw a missionary in the train station with a cardboard sign and a large black velvet yarmulka. When he got into my car he saw a couple of Jews in the car and moved to the next one. He happened to get off and set up shop at the same stop I had to change at so I asked him nicely to please take his yarmulka off so people won’t think he’s Jewish.