The phenomenon you’re looking at is called sequence of tense. It is the topic of substantial research by linguists, but, in a nutshell, past tense matrix verbs (like realized) can take subordinate clauses with either past tense or present tense; however, the nature of the complement plays a substantial role in determining which, if either, is more appropriate.
Ancient mariners realized that the earth isn’t/wasn’t flat, by watching how ships appeared mast first over the horizon.
In cases where the complement is permanently true, speakers generally feel quite comfortable with either past or present tense. Where, however, the complement clause reports something that was true around the time of the matrix event, the complement clause has to anchor its tense to the past tense matrix clause. Hence:
Last month, I walked into the room and saw that Mary was/??is asleep.
For events that last longer than the average bout of sleep (e.g., pregnancy), the present tense is more readily available. Hence, still using last month, you can say:
Mary’s husband only found out last month that she’s pregnant.
But, of course, if the pregnancy is over at the time of utterance, then, again, the past tense becomes obligatory:
Mary’s husband only found out ten months ago that she was/??is pregnant.
For permanent truths, however, like the earth’s not being flat, past tense in the subordinate clause does not imply that the earth has since ceased to be curved. For this reason, it is sometimes called a dummy past