Guys I am running an Axew with the ability rivalry. Now here is my question: I know it deals more damage to POKEMON of the same gender (×1.25),but does it deal less damage to the opposite gender for the same? Should I use it? Please help!
No If opponent is of opposite gender it does 0.75x And if opponent is genderless it has no effect. i.e base power stays at 1x. In game gender is approximately 1:1. You'd be better off with mold breaker.
Source
I don't think it is a good idea. Since most people just have random genders, statistically, you'll probably see both genders equally. Unless there is a really hard gym leader Pokemon like Whitney's Miltank you want to use it on I would not recommend it. Mold Breaker is better.