Consecutio modorum: Do “that” clauses follow an irreal subjunctive in the parent clause?

These Google 5-gram results for "we knew that it was" / "we knew that it were" / "we knew that he was" / "we knew that he were" show no relevant results for the variants using 'were' (though of course many false positives not involving if-clauses elsewhere. These are examples of the string "if we knew that it was" for 2006 - 2019 from the Google Books corpus). The results cover the period since 1800. There is a single (1823) token for "we knew that it were", with an archaic/obsolete usage, 'were' = 'would be':

And while we earnestly prayed for the advancement of his highest interests in time and eternity , we knew that it were mockery to ...

[Memoirs and Select Remains of an Only Son: Who Died November 27, 1821, in ... By Thomas Durant]

This supports my opinion that

• If we knew that it was raining, we would also know that the street was wet.

is the only idiomatic version, and has been for centuries.

The verbs / auxiliaries in the that- (complement-) clauses are in the present (simple) (or other matched constructions, such as 'was' and 'was').

If we knew that it ___ raining, we would also know that the street ___ wet.

This can be either a hypothetical or irrealis conditional, because the past tense knew can refer to simple past

"Since it was raining, the street would be wet. So if we knew then that it was raining, we would also know that the street was wet. Inspector Grimes, did we know that when the report was made?"

or to an unreal (aka "subjunctive") possible world where things are not as they are.

In either case, was is the only correct auxiliary verb for the blanks.

The presenting question, about whether that clauses can follow irrealis verbs, has a simple answer: yes. Verbs govern complement types individually, not by "mood" (which is not a grammatical category in English); and know governs a that complement.

As to whether were should be used in either blank, why bother? Certainly Milne, who has a license, can violate the rules if he likes, and occasionally he does.