We just don’t know.
Lexically speaking, English consistently and traditionally encodes male (he), female (she), a genderless plural (they), and a non-human singular (it). Colloquially, they can also be singular, as can them, although there is plenty of debate around whether it’s truly treated as singular (Foertsch & Gernsbacher 1997, Sanford & Filik 2007, Doherty & Conklin 2017). However, they and them are entirely ambiguous between the singular and traditional plural meanings. I’m investigating themself, which is a nonstandard but (definitively?) singular version of the pronoun. Importantly, as a reflexive anaphor, it must be bound by an antecedent so as an experimenter, I can control what it obligatorily corefers with. This makes it very easy to pair themself (or themselves) with a specific referent whose gender (or gender bias, or lack thereof) can be manipulated. For instance, names, definite and indefinite noun phrases, and indefinite pronouns can be used to test whether different gender biases affect the acceptability of the coreference dependency.
If the Gender Mismatch Effect stems from the genders of two words being incompatible, then we must define what genders are incompatible. Superficially, this is easy because male and female are nice, neat categories, but they aren’t the only genders (and increasingly, are not the only categories). However, if singular they can match in gender with a binary-gender word (either male or female), then we’ve got to be a lot more precise about what we mean when we say the genders of two words match or mismatch, since they is ostensibly gender-neutral. On the other hand, if singular they can’t match in gender with a binary-gender word, but it can match with a gender-neutral word, then maybe we are encoding a third gender category, rather than the absence of gender. This raises the question of how pronouns and gender categories will continue to evolve, if natural gender is gradient but our lexical encoding of it is categorical.
In any case, these are just a few of the possible ways in which gender might be encoded in English, and there is much work to be done.