How gender specific in writing is the character 他
In my experience, when referring to a single subject, I have never seen 他 used as a female pronoun. 她 is used for females, and 它 used for non-gendered or non-human subjects.

Do note that 他 has meanings outside pronouns; it can have the meaning of "other". In these cases, 他 is used and never 她. Examples include 他人 (other people), 他乡 (a place far away from home), 他日 (future).

There are two interesting cases for the 他/她 question though: in the group pronouns 他们/她们 and when the gender is unknown.

For 他们/她们, 他们 is indeed the gender-neutral term. Use this when referring to a group of people (other than yourself and your subject, i.e. "they" or "them"), where their genders are either mixed or not relevant. If you are specifically referring to a group of females though, use 她们. Here's some discussion on this matter. This is in contrast to English which has no gendered "they" or "them".

When gender is unknown, it is more proper to use 他. This is similar to older English style which considered generic he proper usage. Use 他 when in English you would have used "he / she". Note that some people use "他/她" which is perfectly understandable but less proper.

So to summarise:


他 is gender neutral, except in two cases where you would use 她 instead:
When referring to a single female of known gender
When referring to a group of females