When it says hevei makdim es kal haadom b’sholom, it did not say, “unless you are a woman.”
Oomis- when it says al tarbah sicha em haisha, it didn’t say,”except a good morning greeting”.
I don’t think it’s appropriate to greet opposite genders when you’re only passing them on the street.
Of course if someone greets you then you answer back but there’s no reason for you to greet men. But that is your own decision and everyone is responsible over the decisions they make.