Looking at the AMP spec, given the reliance on CSS variables to custom style elements, this means current browser support is narrow. See: Can I use reference
I'm guessing there is a 'graceful fallback' to non custom styled, since browsers not understanding the CSS variables will just ignore that CSS.
Is there a browser compatibility/support matrix for AMP?
Answer
Browser Support
In general we support the 2 latest versions of major browsers like Chrome, Firefox, Edge, Safari and Opera. We support desktop, phone, tablet and the web view version of these respective browsers.
Beyond that the core AMP library and builtin elements should aim for very wide browser support and we accept fixes for all browsers with market share greater than 1 percent.
In particular, we try to maintain "it might not be perfect but isn't broken"-support for the Android 4.0 system browser and Chrome 28+ on phones.
from amp faq
But.. CSS Variables?
The use of CSS custom properties (aka CSS Variables) is polyfilled:
AMP HTML components that are more complex and nested … may be styled with an explicitly defined set of CSS Custom Properties. These are propagated to any children elements that are dynamically created by the runtime, to achieve the desired style.