both of the following true division and multiplication operations crash the
interpreter:

import datetime

class BadFloat(float):
    def as_integer_ratio(self):
        return (1 << 1000) - 1

datetime.timedelta() / BadFloat()
datetime.timedelta() * BadFloat()

this is because both multiply_float_timedelta() and truedivide_timedelta_float()
(in Modules/_datetimemodule.c) assume as_integer_ratio() returns tuple.

i am working on a patch.

BTW, is there anywhere a list of what counts as an extension
module, and what counts as the interpreter core?

I don't know if there is a list, but definitely the parser, the compiler, the evaluation loop, builtin types and few builtin modules (like builtins and sys) are interpreter core. The _datetime module is an accelerator of the datetime module. It is optional and definitely is not in the core.

Please check if there is similar issue with Decimal.

I guess you meant for me to check whether the following has any problem:
import decimal

class BadFloat(float):
    def as_integer_ratio(self):
        return 1 << 1000

decimal.Decimal.from_float(BadFloat())

so it doesn't crash.
if IIUC, this is because the C implementation of Decimal.from_float()
is PyDecType_FromFloat(), while the relevant part of it is a call to
PyDecType_FromFloatExact().
But PyDecType_FromFloatExact() uses float.as_integer_ratio(), and thus
ISTM that the issue doesn't exist there.

(also, the following doesn't raise an exception, as expected:
import decimal

class BadFloat(float):
    def as_integer_ratio(self):
        raise RuntimeError

decimal.Decimal.from_float(BadFloat())
)

New changeset 865e4b4 by Serhiy Storchaka (Oren Milman) in branch 'master':
bpo-31293: Fix crashes in truediv and mul of a timedelta by a float with a bad as_integer_ratio() method. (bpo-3227)
865e4b4

New changeset f37dd11 by Serhiy Storchaka (Miss Islington (bot)) in branch '3.6':
[3.6] bpo-31293: Fix crashes in truediv and mul of a timedelta by a float with a bad as_integer_ratio() method. (GH-3227) (bpo-3654)
f37dd11