Look at this sentence:
I knew that the sky is blue.
To me, it doesn't make sense to say the sky was blue since it still is blue. Even so, is it grammatically incorrect to say I knew that the sky is blue just because the tenses must be the same?
Saying I knew that the sky is blue is correct, assuming the sky is always blue. It is fine to mix the present tense with the past tense when one is expressing a timeless fact. Of course, it is also correct to say I knew that the sky was blue, but that only expresses how the sky was blue back then.
(Yesterday) "I know the sky is blue" said 3125.
(Today) 3125 said he knew the sky was blue.
Your exact words when you spoke yesterday were; "... the sky is blue". However, the time when you uttered those words was in the past i.e. yesterday. You cannot express your thoughts in the past using a present tense. The present tense is also used to speak about facts which are always true e.g; The sun is a star in the centre of the solar system. Water freezes at 0°C. Tuesday comes after Monday. Australia has kangaroos etc.
So you should say: "I know the sky is blue" if it is a fact and you know the sky is always blue. If instead you say,
I knew the sky is blue
you are in fact stating that yesterday you knew without a doubt the sky is blue. Since then however, your certainty has changed and effectively speaking, you don't know if it is true any more (yesterday you knew the sky is blue but today you don't know). The sentence is grammatically correct but it struggles to make logical sense.