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PyMem_Raw* APIs should be thread safe. But in debug mode, they are not that simple and increment a global variable *serialno* and the incrementing action is not thread safe.

I looked at _Py_atomic_address to avoid atomic "serialno++", but we don't have atomic_fetch_add(). We could implement it using a loop and atomic_compare_exchange_strong()... but we don't have atomic_compare_exchange_strong() neither.
I tried to add a mutex, but there are some pratical issues:
* bpo-35388: question about calling Py_Initialize() / Py_Finalize() multiple times
* I modified _PyRuntimeState_Init() to initialize the lock.
_PyRuntimeState_Init() calls PyThread_acquire_lock() which calls PyMem_RawMalloc(). Problem: PyMem_RawMalloc() requires the lock. I worked around the isuse using "if (_PyRuntime.mem.mutex != NULL) {".

By the way, the previous attempt to add _PyRuntime.mem had to be reverted. See bpo-32096, bpo-30860 and the commit:
commit 9e87e7776f7ace66baaf7247233afdabd00c2b44
Author: Victor Stinner <victor.stinner@gmail.com>
Date: Fri Nov 24 12:09:24 2017 +0100
 bpo-32096: Remove obj and mem from _PyRuntime (#4532)
 
 bpo-32096, bpo-30860: Partially revert the commit
 2ebc5ce42a8a9e047e790aefbf9a94811569b2b6:
 
 * Move structures back from Include/internal/mem.h to
 Objects/obmalloc.c
 * Remove _PyObject_Initialize() and _PyMem_Initialize()
 * Remove Include/internal/pymalloc.h
 * Add test_capi.test_pre_initialization_api():
 Make sure that it's possible to call Py_DecodeLocale(), and then call
 Py_SetProgramName() with the decoded string, before Py_Initialize().
 
 PyMem_RawMalloc() and Py_DecodeLocale() can be called again before
 _PyRuntimeState_Init().
 
 Co-Authored-By: Eric Snow <ericsnowcurrently@gmail.com>

See also bpo-35265: "Internal C API: pass the memory allocator in a context".
The most complex part is the Python initialization which changes the memory allocator *and* allocate memory. We have to remain which allocator has been used to allocate data, to be able to release memory at exit.

Note: PTHREAD_MUTEX_INITIALIZER can be used to statically initialize a mutex.

See also bpo-35368: [2.7] Make PyMem_Malloc() thread-safe in debug mode.

Python 3.8 has been fixed. I disabled serialno field by default: PYMEM_DEBUG_SERIALNO is not defined by default. You have to opt-in to get this bug :-) I don't see any easy fix older Python versions. I close the issue.