This is incorrect fix. If size differs, it will silently skip remove operation - which is hard-to-recognize error.

I suggest to lock both index and remove operation using self.borrow_vec_mut() if possible.

I implemented it this way because list.remove returns None in CPython.

>>> class rewrite_list_eq(list):
...     pass
... 
>>> 
>>> class poc:
...     def __eq__(self, other):
...         list1.clear()
...         return self
... 
>>> 
>>> list1 = rewrite_list_eq([poc()])
>>> print(list1.remove(list1))
None

But as you said, this is hard-to-recognize error.
Should I fix this so that list.remove returns ValueError?

The bug is broken sync between index and remove. out of index is one of the visible example of it. e.g. when l = [0, 1, 2, 3] and tried l.remove(3), del l[0] can be done between index and remove. Then it is the case you described. When user ran l.remove(3), they expect 3 is gone. This is the reason I said hard-to-recognize.
But what if l.insert(0, 0) happened instead of del l[0]? Then it will remove 2 instead of 3. This is the original bug. Your fix is about only the case l.remove(3), but not applicable to other cases.
Instead of it, we'd better to synchronize index and remove.

Then it will remove 2 instead of 3.

Unless I'm misunderstanding your comment, this is also how CPython handles it, a user doing weird things in __eq__ can't really expect sensible behavior:

>>> class BadEq:
...     def __eq__(self, other):
...             if isinstance(self, type(other)):
...                     l.insert(0, 0)
...                     return True
...             return NotImplemented
... 
>>> l = [10, 20, BadEq()]
>>> l.remove(BadEq())
>>> l
[0, 10, <__main__.BadEq object at 0x7f450686e070>]

As far as I can tell from list_ass_slice they check/force that the value for the index (ilow and ihigh) is in bounds for the list and then perform the operation.

Ah, thank you. And sorry for wrong comment. I needed to check how cpython handle it first.

So is this version compatible to CPython @DimitrisJim ?

It definitely gets us closer, we definitely shouldn't panic when the list changes size underneath our feet.