Since you asked for "any words of advice", I'll start here: exes should do whatever they can NOT to involve their kids in conflicts between the two parents, no matter what the age of the children. Where such conflicts already exist, parents should also try NOT to escalate/heighten those conflicts or get the kids further involved in them. Particularly at the holidays.
I've learned from first-hand experience & many years of close observation that kids of all ages usually experience criticism of one parent by the other parent as extremely painful & hard to bear. Since children are hardwired to love & identify with both parents, castigating either mum or dad tends to make them feel personally attacked - & extremely torn/conflicted.
So please don't sink down to your ex's level by telling your kids he's an idiot or poorly-educated nitwit who knows nothing, no matter how much your ex might deserve such descriptions. Vent about him & his "ill educated views" to your friends & on boards such as this. But not to your kids, especially if they are still minors.
If you're kids are still kids, you'll have plenty of time to explain feminism from your POV - which I hope you'll do in appropriate ways at junctures in the weeks, months, years ahead. But right now I'd suggest you find a way to gracefully (& with humour) segue away from the contentious issues at hand - what feminism is & whether those of us who ascribe to it are all man-hating tyrants out to rule the world - & reassure your children that you & their dad love them & both of you will always do so even though you clearly disagree with each other about a lot of other things.
I can't be more specific without knowing the ages of the children. But what's best for them should always come first in these sorts of situations, & that usually means calming troubled waters rather seizing the opportunity to prove you're right & your ex is a jerk. Showing your kids that it's possible to be good-natured, gracious, civil & even humble when castigated by others might be the best holiday gift you can give them.