Okay but, something funny to consider: Jax and Gill's Dad was a fairy tale buff. He taught his kids that all stories are true.
Thus, Jax already KNOWS the legend of the Silver-Eyed Warriors, but also probably has a VERY skewed idea of what Ruby's actual abilities are.
Something to consider about this is that it's pretty clear at this point that NOBODY has any real solid idea what exactly Ruby's, or the rest of the Silver Eye Warriors actual abilities are. Even Ruby and Maria, who have more information on the topic than literally ANY Silver Eyed Warrior in history thanks to Jinn, only have a pretty basic theory as to the origins of their eyes, which itself is clearly only a small piece of the story. I've explored this in previous posts already, but I'm positive at this point that there is a LOT more to the Silver Eyes than just 'anti-Grimm lasers' that Ruby will be figuring out going forward.
But going back to your point, yeah it's pretty fun to imagine what Jax's reaction to Ruby might be. Dude's spent most of his life at this point on an ego-trip in his personal hype-train building up that he's got this big, important noble 'destiny' as the 'true king of Vacuo'.
Buuuttt, NOW he's found himself 'opposed' by someone who isn't just some rival leader with a local cult of her own, but who is uniting the entire world. A girl who seems to have a background steeped in the greatest legends of Remnant's past. A girl who seems to have a heroic destiny so great it likely makes even Jax's delusions of grandeur seem small and petty by comparison. And that's not even going into what Jax might believe the Silver Eyed Warriors to be capable of.
Basically, I get the feeling that Jax's view of Ruby is probably going to be somewhere between 'seething, obsessive jealousy' and 'abject TERROR'. XD