Claude Code wraps both the AGENTS.md and CLAUDE.md in a system-reminder with this disclaimer at the bottom:

IMPORTANT: this context may or may not be relevant to your tasks. You should not respond to this context unless it is highly relevant to your task.

Codex follows the AGENTS.md far better. CC seems to have nudged people away from taking the CLAUDE.md as mandatory instructions.

This bug was closed Not Planned and from a recent analysis of the system prompt the behavior is still there even with the new inclusion of AGENTS.md.

https://github.com/anthropics/claude-code/issues/18560