I played around a bit with WPT's H2 support and I found that Chrome is quite restrictive on header values, unless I'm missing something. Basically, if they contain (after stripping leading and trailing HTTP whitespace, which includes newlines) anything but:

• 0x09
• 0x20 to 0x7E, inclusive

there's a network error.

This is for responses. I haven't checked requests (the API allows 0x80 and friends).

Firefox is a lot more permissive.

Restricting this seems reasonable, though we cannot really change the API (should there be an opt-in? probably not) or HTTP/1 behavior. If HTTP/2 (and HTTP/3?) do not require this already then perhaps Fetch should. At the very least it seems worth mentioning around the definition of header value.