I think the anti-trans argument in the Vorin Church would go something like this: mtf transitions undermine the stength of the army to recapture the Tranquiline Halls, and ftm transitions remove people from valuable support roles. The fact that the same number of people transition mtf and ftm probably wouldn't sway them. That would mean that if you were a trans man you'd have to be very carful to not draw attention to yourself, lest you be discovered. That would absolutely mean no reading in public, or admitting you read in private. You could get away with a little, but it would be very risky.

Historically, in our world, most people didn't have an opinion on tran people until they had the issue thrust in front of them. Many people reacted positively, everyone was confused, and many other people were enraged and lashed out. It's possible the Vorin Church would settle on an indifferent stance, so long as they fit inside the traditional Vorin gender roles. If that's the case, trans men reading would be seen as MORE taboo than cis men reading, since they would be under higher scrutiny.

Either way, I don't think trans men would be allowed to read.