Just because you decided to consider this problem imaginary, it does not mean that this problem does not exist in the real world, bringing suffering to millions of disenfranchised women.
Regardless of the time period, I would simply propose focusing on educating current and future generations that men and women have equal rights.
If you dig into history a bit, you’ll find that state-sponsored persecution - ethnic, religious, or otherwise - is almost always guaranteed to backfire in the long run.
Is it any less propaganda just because you agree with it?
Educating people of what? "Gender equality is good" is a normative statement.
And nitpicking aside, my point stands entirely, whether it's "propaganda" or "education".
I definitely simplified things a bit, but you can educate people on how to conduct themselves over the long term through various mechanisms. Many countries used this approach effectively to solve actual societal issues; however, the hijab is not a societal issue in and of itself.
It may have a religious origin but a headscarf is a fashion accessory. Like trousers or shirt buttons. We could ban them too, just for fun!
Up with skirts! Down with trousers!
See? What fun!
Do you also apply that logic to Sikh turbans (dastar)? In other words, do you believe that forbidding Sikhs from covering their hair is not religious persecution? How do you think Sikhs would react to that?
Edit: Or wait, I might have misunderstood: do you actually think that a hijab is equivalent to a generic headscarf? If so, it is not - please read a bit about it before commenting further.
The niqāb is problematic. I find it difficult to talk with some one when I cannot see their face. (Then there was Covid....). I am not sure if that is a personal quirk or a basis for a justifiable fashion law!
And of course a hijab is a headscarf. Not just a head scarf, like a turban is a hat, not just a hat. Why would we want to ban either?