In Japanese there is a word called "看護師" which basically is a gender-neutral way of referring to a nurse.
I was wondering, Is there such an equivalent word in English; that is, is there a gender-neutral way of referring to a nurse?
Note that gender isn't sex. It's a linguistic/grammatical notion and there are languages with more than three genders:
English doesn't have a grammatical gender, outside of pronouns like he, she it. The Wikipedia article above gives a citation for this claim: http://en.wikipedia.org/wiki/Grammatical_gender#cite_note-enc-0
What's at issue here is that there is a lingering sex-role stereotype attached to nurse. This is not easy to expunge, and is still carried to some extent even by a politically-correct term such as health care professional. Some people will imagine a woman when they hear health care professional, without any further context, and there is nothing that can be done about that. Simply adding health care to professional brings in stereotypes related to the profession in which the supporting, caregiving roles are occupied largely by women.
Also, consider the word "stripper": paint stripper, stripper, male stripper. You can see there is no gender in the word word itself: a stripper is something or someone that strips, transitively or reflexively.
I was wondering, Is there such an equivalent word in English?
i.e. What's a gender-neutral way of referring to a nurse ?
You don't really need an equivalent word. The word nurse means both men or women who do that job.
If certain people associate the word with women, that's their personal view. It does not mean that the word itself is particular to women, at least not in modern times within the UK.