Given the fact that you want to do a lot with your CSS, it doesn't make much sense to choose a "native" option like React Native or Weex or whatever (apart from the fact that you're not a React fan, and that Weex isn't that mature yet). You'd be creating more problems than solving, especially since you're more comfortable with web dev (typically with RN you're still often venture into native dev).
Apart from that, I think it's pretty safe to predict that within a few years web dev and PWA's will become a popular choice over "native" for a certain class of mobile apps. If your app doesn't require native (but check your requirements thoroughly) there isn't much reason to go "native".
So if your choice is (a) web dev, (b) Vue then what are the options?
I'd give Quasar a serious look, it's a mature and professional framework with great documentation and a nice community. Allows you to build for PWA, Cordova and Electron with one code base. It's been called "the Ionic of the Vue world" (mentioning that because you talked about Ionic).
Yes, it ships with 2 standard "themes" (Android/Material and iOS) and it wasn't clear to me how feasible it is to develop your own theme. The iOS theme on the other hand looks fairly "neutral" (doesn't jump out like Material Design does) so probably you could just take that and customize it.
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