I wrote “in large part”, not “always”.
Of course there are some issues where there should be more support for men. But I am pretty sure female to male domestic violence is not at the top of the list on why these people vote conservative. The conservative “solution” would be to shut down male AND female support in that regard.
I will gladly support any initiative for more equality in the justice system (even though we are probably not even in the same country).
I am not aware of any initiatives, though. The conservative focus, depending on the country, seems to be on hating foreigners or banning abortions. So I am not sure why anybody would want to vote conservative if they want an equal justice system.