Raising for order=True if one of the ordering dunders exists sounds fine.

I am confused by the corner case for hash. Your table:

"""
eq=?	frozen=?	__hash__
False	False		do not generate __hash__
False	True		do not generate __hash__
True	False		set __hash__ to None unless it already exists
True	True		generate __hash__ unless it already exists
                         and is None
"""

Then you write at the end of that message:

"""
One special case to recognize is if the class defines a __eq__. In this case, Python will assign __hash__=None before the dataclass decorator is called. The decorator cannot distinguish between these two cases (except possibly by using the order of __dict__ keys, but that seems overly fragile):

@dataclass
class A:
    def __eq__(self, other): pass

@dataclass
class B:
    def __eq__(self, other): pass
    __hash__ = None

This is the source of the last line in the above table: for a dataclass where eq=True, frozen=True, and hash=None, if __hash__ is None it will still be overwritten. The assumption is that this is what the user wants, but it's a tricky corner case. It also occurs if setting hash=True and defining __eq__. Again, it's not expected to come up in normal usage.
"""

I think I understand what you are saying there -- the two cases are treated the same, and a __hash__ is created (assuming the decorator is really "@dataclass(eq=True, frozen=True)"), overwriting the "__hash__ = None" for class B.

However the table's last line says "generate __hash__ unless it already exists and is None". Perhaps that was a typo and you meant to write "and is *not* None"?