Currently, Chrome, Edge, and Safari all set the mode of the current document that's being processed through document open steps to no-quirks mode. Firefox does not, however.

The current call to set mode to no-quirks in WebKit was from https://bugs.webkit.org/show_bug.cgi?id=44788, but it's possible that the behavior has been there since even before that patch. I cannot find a corresponding call in the HTML Standard from that era.

Tests I used to confirm this: https://github.com/TimothyGu/document-open-tests (the ones starting with step-undef-no-quirk)

WPT (still being worked on): web-platform-tests/wpt#10679