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In the .py implementation of datetime.replace (and date.replace and time.replace), the new datetime is created using the datetime type:
https://github.com/python/cpython/blob/master/Lib/datetime.py#L1578
But in the C source, it is created from type(self):
https://github.com/python/cpython/blob/master/Modules/_datetimemodule.c#L5046
I think the second should be the preferred behavior, so the datetime.py source should be updated to reflect that it's calling self.__class__(...) rather than datetime(...). I can prepare a PR if this would be desirable.
(That said, I'm not 100% clear under what circumstances the code in datetime.py is actually *used*, so I'm not sure how to write tests for it - is datetime.py essentially documentation, or is there a way to explicitly fall back to it?)
Per this issue on the pypy3 tracker:
https://bitbucket.org/pypy/pypy/issues/2635/datetimereplace-always-returns 

I agree that returning type(self) or self.__class__ (not sure which is better) is the right thing to do.
It might be possible to argue that the Python version is buggy, if the C version is treated as the reference implementation and the Python version has to duplicate that. Or if the documentation specifies the C version's behaviour.
But if the precise behaviour is unspecified, or if the Python version is the reference implementation, its best to treat this as an enhancement rather than a bug fix and only apply it to 3.7.
I'm not sure which is the right approach here.

See also issue 20371.

@r.david.murray In the other thread, you mention that the full test suite is run against the C and Python implementations, so that answers the question of how to write the tests.
I think treating it as an enhancement in Python 3.7 makes a reasonable amount of sense - it's clearly under-specified at the moment and people are probably relying on the CPython behavior (dateutil definitely is in the latest stable release, but not on master). Saying "it's implementation-specific before Python 3.7 but in Python 3.7+, the spec says it should use self(type)" is fine by me. It's not particularly hard to work around if you're subclassing datetime anyway.
Among the major libraries that provide their own datetime objects:
- Arrow seems to use composition (https://github.com/crsmithdev/arrow/blob/master/arrow/arrow.py)
- pendulum subclasses, but implements their own "replace": https://github.com/sdispater/pendulum/blob/master/pendulum/pendulum.py#L25
- delorean uses composition: https://github.com/myusuf3/delorean/blob/master/delorean/dates.py#L174
- maya uses composition: https://github.com/kennethreitz/maya/blob/master/maya/core.py#L72
I'd say for the most part it's not a major issue to change it even as a bugfix, particularly if the line we're going with is "it was always implementation-specific", but there's also no rush.

Some time ago this was fixed in pypy3:
https://bitbucket.org/pypy/pypy/issues/2635/datetimereplace-always-returns
I made a PR fixing this for `datetime`, `date` and `time`.

New changeset 191e993365ac3206f46132dcf46236471ec54bfa by Victor Stinner (Paul Ganssle) in branch 'master':
bpo-31222: Make (datetime|date|time).replace return subclass type in Pure Python (#4176)
https://github.com/python/cpython/commit/191e993365ac3206f46132dcf46236471ec54bfa

New changeset b9a40aca2935d2569191844c88f8b61269e383cb by Victor Stinner (Miss Islington (bot)) in branch '3.6':
bpo-31222: Make (datetime|date|time).replace return subclass type in Pure Python (GH-4176) (#4356)
https://github.com/python/cpython/commit/b9a40aca2935d2569191844c88f8b61269e383cb

Thanks Paul Ganssle for the bugfix! I merged your PR and backported it to Python 3.6. (Python 3.5 doesn't accept bugfixes anymore.)