Taken in isolation, the idea of the 'side saddle riding men' makes sense with a certain view of logic.  It is the reasons behind the decision and the culture it was created in that makes it intolerable nonsense.

The 'Star Trek Logic' comment from above is apt: creating a setting where certain 'normal' conventions are reversed is a tried and true fiction technique.  Doing so with a particular agenda, and with a certain smug satisfaction at having tweaked people's nipples, or even having 'proven' some sort of political point is, to be frank, assanine and juvenile.

The idea of men riding side saddle to protect 'the boys' is no more absurd than women having to do the same to protect their virtues. Or, rather, less so.  Its silly either way.

Not having read Reign, and only dimly remembering the rest, I must veture on a limb to point out that this single alteration of setting 'givens' does not, and would not, render men 'impotent' on the battlefield, and the simple biological metric that males are the more expendable gender in reproductive math would require far more than a simple idiot idea (ride side saddle to protect 'the boys') to overturn.   Rather than put women on the front lines of war any number of other solutions present themselves: Cavalrymen are made up of older, established 'gentlemen', cavalry are Jannisary style eunuchs... cavalry fight side saddle and damn the poor leverage!, Use Chariots Moar. Whatever.

Interestingly enough I've read through Reign and don't ever remember stumbling across that side saddle crap.  Who knew, all this time I've been playing the game wrong.  Rant = Ridiculous.