How people "feel" (regardless of their first language) can be quite subjective, and in a linguistic context even the word "feel" can have multiple interpretations. As such, a single English-speaker, picked at random, may associate with any of these geographical names a particular gender based on analogy with similar/familiar terms. For example, names of female individuals often (of course, not always) end in
/ə/ (orthographically ⟨a⟩), e.g., Andrea, Antonia, Erica etc., and this may cause some individuals to build a feminine association with names like California or America. [In North Carolina, where I live, I have often heard of people refer to the state as a 'she' or 'her'.] But this should not be taken to imply that such words have a particular gender, since English definitely lacks grammatical gender, except in pronouns, which the answer by @fdb addresses.
Now, I don't identify as a native English-speaker, but I do speak English like a native, and more importantly, my first language is genderless (more so than English; we even lack gendered pronouns), and I can vouch for the fact that while I may sometimes refer to a geographical/political location as masculine or feminine, I certainly do not associate with these any notion of actually possessing any biologically female or male attributes, the way I would for human beings or even some animals – at least, not in the way a Russian- or German-speaker would.