If thar were the case, what sorts of duties would such a position entail?

Only if the selection of the minister is based on a public vote. A male cat will be filling the seat in no time.

Women have a minister to support women's issues in the government. Men get to walk the streets of major cities at night without fear, and get respect and good pay in their careers. As a man, I feel like I'm getting the better end of the stick, even without ministerial support.

Women have been systematically pushed down for thousands of years, and now they have systems to help bring them back up. It's like being upset someone else gets crutches, because you'd like support too. I mean, sure, wear comfortable shoes, but you don't need support as much as they do. I look forward to the day nobody need crutches.

nooo that would be sexist /s

I'd say theoretically yes. But don't make it two, make it three or you'll again exclude people.

But that minister then has do do their job properly and not just hate on feminism and try to make their lives difficult and do some culture/gender war.

If you want to do it properly find out first how many things there are to do regarding gender. And if maybe one person can work on gender issues. It seems unlikely to me that you need so many people for one topic. Only have many people if it's impossible for them to simultaneously work for men and women.