Your parents cannot accept that they bet on the wrong horse so it doesn't matter what the facts are. Due to cognitive dissonance, they will automatically reject any information that conflicts with their belief system.
It's so ridiculous because they go door to door telling people to get out of false religion, but they never question their own beliefs. The bible says to "keep testing as to whether these things are so", but anybody that asks questions is vilified. If what they have is "the truth", it should be easily proved, lies should be easily disproved, so why are they so afraid of "apostate lies"?
This is why they demonize so called apostates (a word not even in the bible). They are afraid because they know they are wrong. If their arguments for 607 were sound, they could easily publish a book or pamphlet refuting the 587 date reasoning, laying it all out so that anyone could understand it, but they don't because they cannot defend the 607 date.