Finally figured it out, thanks to @rapropos 's comment on this thread here.
The issue was indeed related to webpack, and got fixed in this commit, which is included in v0.0.46. I was using @ionic/app-scripts v0.0.45.
To fix, simply run npm install @ionic/app-scripts@latest --save-dev.
Note however that there is currently a problem in v0.0.46 related to copying fonts (see issue 475 and 448), so you’ll need to manually copy them until the issue gets fixed.