Men have the option as far as I know. I would advise you check your local rules or check with the show holding body or disciplines ruling body.
it’s about level as opposed to gender. If you’re doing eventing dressage, you only need a stock tie if you’re doing above novice as jackets are optional and you can’t really wear a stock tie without a jacket. I could be wrong so I recommend checking with a coach or anyone who would know. I don’t know the rules for non-eventing dressage though.