A Masorti woman in Israel wishes to write a mezuzah. She knows how. May she?
The sources all, from the gemara up, say that writing tefillin and writing mezuzot are halakhically inextricably linked, and that only someone hayav in tefillin and faithful in its observance is kosher to write mezuzot. (More detail here.)This is what determines who is kosher to write sifrei kodesh. Considerations such as obligation in mezuzah, talmud Torah and so on do not come into it; only the mitzvah of tefillin is relevant. In classical interpretations, this excludes women.
Including women in Jewish ritual is usually founded on one of two premises. The first may be summarised: Bother all this stuff about obligation, we’re going to do what we like, and we’re going to let women do what they like as well. I personally don’t think this approach ought to be applied to the holy books. The other egalitarian premise, then, rests on the idea that contemporary women may have equal status vis-a-vis obligations to men. Some assume that women are born thus obligated, some hold that the obligation must be assumed. Either way, obligation is key. If – emphatically if – we hold that women and men have equal obligation in the mitzvah of tefillin, the all-important baraita on Gittin 45b does not automatically exclude women, so she theoretically may write a mezuzah. If your correspondent does not consider herself obligated in laying tefillin, I personally would not view any mezuzah written by her as kosher.
Further, the baraita also excludes people who are obligated in the mitzvah but are not faithful about performing it. Thus, even if your correspondent is basically egal, if she does not lay tefillin on a regular basis, she is pretty much as unsuitable to write mezuzot as if she were a non-Jew. One can use selective interpretation to argue otherwise; I personally would be strongly disinclined to give a heter to write mezuzot to someone who is not particular about laying tefillin. Mezuzah writing is one of the most formalised mitzvot there is; it seems strange to me that someone would on the one hand adopt this formalism and on the other hand seek its rejection. A convincing articulation of why the one does not automatically exclude the other might cause me to reconsider.
If she is committed to the mitzvah and particular about its performance, and thus in my view permitted to write mezuzot, in any case she should bear in mind that this reasoning rests on the assumption that women’s obligation in time-bound mitzvot can be elevated to a d’oraita level. Especially in Israel, but in general in the halakhic world, this is not accepted reasoning. To any non-egal community, absolutely she cannot write a mezuzah. For egalitarian communities, she should go right ahead and good luck to her.