That doesn't match with my understanding of free-threaded Python. The GIL is being replaced with fine-grained locking on the objects themselves, so sharing data-structures between threads is still going to work just fine. If you're talking about concurrency issues like this causing out-of-bounds errors:
if len(my_list) > 5:
print(my_list[5])
(i.e. because a different thread can pop from the list in-between the check and the print), that could just as easily happen today. The GIL makes sure that only one python interpreter runs at once, but it's entirely possible that the GIL is released and switches to a different thread after the check but before the print, so there's no extra thread-safety issue in free-threaded mode.
The problems (as I understand it, happy to be corrected), are mostly two-fold: performance and ecosystem. Using fine-grained locking is potentially much less efficient than using the GIL in the single-threaded case (you have to take and release many more locks, and reference count updates have to be atomic), and many, many C extensions are written under the assumption that the GIL exists.