I think it's more likely the old composers took the old part names and adapted them to congregational music. It's not that Shape note singers (we're talking Americans in the late 1700s, early to mid 1800s) didn't accept women in the congregation, it's that folks like Tallis had called the top part the "treble", and the creators of new tunebooks didn't bother to change the name of the part. So IMO shape note music has probably always accepted women on the treble part.

The alto part seems to be a different story though. In fact, in one of the old shape note tune books I've got (a reprint of The Southern Harmony, originally from 1854), the alto part is labeled "counter", suggesting it was adapted from the Reformation-era countertenor parts. It was occasionally sung by boys, or by women, but often left out entirely (most of the tunes in the Southern Harmony are three part, with no alto). Later on, this "second part from the top" reemerged as a standard alto part, labeled as such, and sung by only women and possibly boys (but by this time, certainly not men in falsetto).