Japanese has the property you describe, depending on how you analyze its sort-of pronouns. Also, according to the article
kanojo 彼女 (f) was consciously introduced, but not recently.
Pronouns are really low-frequency words in Japanese compared to other languages, but it has two gender-specific third person pronouns
kare 彼 (m) and
kanojo 彼女 (f). These words also have other uses. There's also an alternative
ano hito あの人 (lit: that person) that is gender-neutral.
Based on your question, I'm assuming you are looking for a natural language precedent for something a bit like Ido's pronoun system.
Ido does not have grammatical gender in its nouns, but does have a system of optional grammatical gender in its third person pronouns. However, it also has a
singular and plural epicene pronoun that explicitly does not comment on the gender of its referent.
il(u) -- 3sg masc
el(u) -- 3sg fem
ol(u) -- 3sg neut
lu -- 3sg epicene
ili -- 3pl masc
eli -- 3pl fem
oli -- 3pl neut
li -- 3pl epicene
Your question is difficult to answer because the property you want is in some ways incompatible with languages with a prototypical gender system. In a prototypical gender system, every noun is assigned a grammatical gender and the noun's gender is reflected morphologically on determiners, verbs, or adjectives and not just in the pronoun system.
So, languages with grammatical gender frequently have cases where the assigned gender of the noun conflicts with semantic properties of the referent. For instance, in French, a man is still
une personne. In cases like that, it is acceptable in French to use the gendered pronoun matching the formal class of the noun. I'm not a native French speaker. I don't know off the top of my head whether it is totally impermissible to use a masculine pronoun to refer back to a masculine entity introduced as
une personne previously if you later establish this person's masculineness somehow in the discourse without explicitly using a masculine noun to refer to them.
The point is: grammatical gender is a formal property of every noun. An explicit
don't-care pronoun whose semantic range overlaps with gender-specific pronouns sort of conflicts with this.
Additionally, purely pronominal gender systems are rare to begin with.
Our examples have involved agreement of the verb, but there are
various other targets which may agree in gender, such as adjectives,
determiners, numerals and even focus particles. Most scholars working
on agreement include the control of anaphoric pronouns by their
antecedent (the girl ... she ) as part of agreement. If this is
accepted, as we do here, then languages in which free pronouns present
the only evidence for gender will be counted as having a gender
system. Of course, such languages with pronominal gender systems have
a much less pervasive system than those like Russian. Including them,
however, makes little difference to the overall picture, since they
are rare (the best known example is English, which is typologically
unusual in this respect); another is Defaka (Niger-Congo; Niger Delta,
Nigeria; Jenewari 1983: 103-106).