`RuntimeError: Attempted to exit cancel scope in a different task` when cleaning up multiple MCPClient instances out-of-order

Describe the bug
If two MCPClient objects are instantiated and cleaned up in non-FILO order (i.e., the first-created client is cleaned up before the second), teardown fails with a cascade of RuntimeError/CancelledError exceptions coming from anyio and mcp.client.stdio.

To Reproduce
Minimal repro:

import os, asyncio, json
from typing import Optional
from contextlib import AsyncExitStack
from mcp import ClientSession, StdioServerParameters
from mcp.types import TextContent
from mcp.client.stdio import stdio_client

class MCPClient:
    def __init__(self, command: str, args: list[str], env: Optional[dict] = None):
        self.session: Optional[ClientSession] = None
        self.command, self.args, self.env = command, args, env
        self._cleanup_lock = asyncio.Lock()
        self.exit_stack: Optional[AsyncExitStack] = None

    async def connect_to_server(self):
        await self.cleanup()
        self.exit_stack = AsyncExitStack()

        server_params = StdioServerParameters(
            command=self.command, args=self.args, env=self.env
        )
        stdio_transport = await self.exit_stack.enter_async_context(stdio_client(server_params))
        self.stdio, self.write = stdio_transport
        self.session = await self.exit_stack.enter_async_context(
            ClientSession(self.stdio, self.write)
        )
        await self.session.initialize()

    async def cleanup(self):
        if self.exit_stack:
            async with self._cleanup_lock:
                await self.exit_stack.aclose()
                self.session = None
            self.exit_stack = None

async def main():
    cfg = {
        "command": "npx",
        "args": ["-y", "@adenot/mcp-google-search"],
        "env": {
            "GOOGLE_API_KEY": os.environ["GOOGLE_API_KEY"],
            "GOOGLE_SEARCH_ENGINE_ID": os.environ["GOOGLE_SEARCH_ENGINE_ID"],
        },
    }

    c1, c2 = MCPClient(**cfg), MCPClient(**cfg)
    await c1.connect_to_server()
    await c2.connect_to_server()

    # Works (FILO)
    # await c2.cleanup()
    # await c1.cleanup()

    # Fails (FIFO)
    await c1.cleanup()      # <-- boom
    await c2.cleanup()

if __name__ == "__main__":
    asyncio.run(main())

Expected behavior

cleanup() should succeed regardless of the order in which multiple MCPClient instances are closed, as long as each instance’s own exit_stack is intact. A single client ought to manage its own lifetime without depending on external FILO discipline.

Actual Traceback

RuntimeError: Attempted to exit cancel scope in a different task than it was entered in
...
asyncio.exceptions.CancelledError: Cancelled by cancel scope ...
...
RuntimeError: Attempted to exit a cancel scope that isn't the current task's current cancel scope

Environment

Commencez par exécuter la reproduction minimale dans l’issue, puis examinez le comportement de MCPClient.cleanup(), AsyncExitStack, stdio_client et du teardown de ClientSession. Le correctif est terminé lorsque des clients créés indépendamment peuvent être nettoyés dans l’ordre FIFO sans RuntimeError ni CancelledError, tandis que le nettoyage en ordre FILO continue de fonctionner.