If I want to do something and/or go somewhere and partake in something that is permissible, but I just don't want anyone to hassle me about being Jewish, am I allowed to wear a baseball cap or some other nondescript head wear, instead of a kipah?
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It seems to be that the answer depends on the effect that a baseball-cap covering your head has on you. From what I understand, the reason why we cover our heads all day is because of the gemara in Shabbat (156b) which says:
(My) translation: "Cover your head so that there will be on you fear of heavens"
which is quoted in the Shulchan Aruch as Halacha (O"C 2:6). If a baseball cap indeed imbues you with a sense of "fear of heavens," then it should be enough to fulfill the words of the gemara. (On the other hand, if your standard kippa does not fulfill this gemara, perhaps you should move on to a more extreme option.)
The cultural aspect of a kippa, from what I understand, (of course I may be completely wrong,) is outside the boundaries of Halacha, which makes it difficult to address definitively. Nowadays, when a kippa has become the symbol of an Orthodox Jew, I could see how some may compare hiding it to מושך עורלתו- someone who covers up his Berit Mila because he is ashamed to be in a covenant with God, which is a very serious offense (Rambam Teshuva 3:6), but I don't think that Halachically it can be classified as such, considering that Halachically it doesn't represent a Jew, the way a Berit Mila does.
(I think that it goes without saying, though, that CYLOR is pretty applicable here.)
HaRav Haim Levi Shelit"a (Anshe Hayil 1:55) says hats count for a head covering.
I have been told that the head should be covered at all times. This being said I don't always wear a Kippah as a hat seems to work just fine and protects my face from the sun's rays. If you wear the head covering as a fulfillment of the requirement, and not to blend-in with the crowds then the answer is yes, wear your cap, hat or whatever. If you are afraid of looking like a Jew by wearing a Kippah and wish to trade it for a hat in public then I would advise against the hat and go talk with your Rabbi. Some places of work will not allow Kippah (Mining, construction, etc...) If would then be assumed that any head covering allowed by the place of work should be used. Some of us also wear both, the Kippah underneath the hat to gain the benefits of both.