fix: optionize initialized notification tolerance

[elainegan-openai]

Summary

• add an explicit MCP streamable-HTTP option for tolerating failed initialized notifications
• keep the default strict and only ignore the failure when callers opt in
• implement the option by wrapping the configured httpx_client_factory, rather than forking MCP's stream client orchestration
• add focused transport and wiring coverage for the new option

Why

Best-effort notifications/initialized POST could fail and poison the transport, even though subsequent real requests could still succeed. This change keeps the behavior opt-in at the SDK layer so apps can choose the more tolerant transport policy explicitly.

Validation

• ruff check src/agents/mcp/server.py tests/mcp/test_streamable_http_client_factory.py
• PYTHONPATH=src pytest -q tests/mcp/test_streamable_http_client_factory.py

[seratch]

The overall direction makes sense. Making only the notifications/initialized request best-effort, behind an explicit opt-in flag, is a reasonable approach, and it correctly avoids hiding failures for other requests.

My main concern is the implementation layer. Right now, this change depends on create_mcp_http_client from mcp.client.streamable_http, which is not part of that module’s exported public surface and already breaks mypy. It also replaces httpx.AsyncClient._transport, which is a private attribute and therefore somewhat brittle.

A cleaner solution would be to handle this directly in the MCP Streamable HTTP transport, where the code already knows when it is sending the initialized notification. That would avoid re-parsing raw HTTP request bodies, avoid private httpx internals, and keep the behavior closer to the protocol logic.

So my recommendation would be:

1. For a quick fix, keep the current behavior but remove the non-exported import issue and make sure the full typecheck/test gate passes.
2. For the better long-term solution, move this tolerance into the upstream transport layer and let the SDK only pass through the opt-in flag.

It would also be good to add a test covering the combination of ignore_initialized_notification_failure=True with a custom httpx_client_factory, to ensure headers, timeout, and auth are still preserved correctly.

[elainegan-openai]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. 👍

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