I came across the sentence "It's been thirty years since my parents first met." I am sure that if I heard "It's been thirty years that my parents first met", I would accept it as grammatical, but I can't find any reference to support this. Am I wrong?
You'd have to use present perfect on both sides for that sentence to work:
Otherwise, remove the present perfect from the first part:
In both examples, as well as the ones you referenced, that acts as a conjunction, or should. If you are trying to use it as a determiner, then it simply doesn't work there.
In your example, you would have to use the word since.
Using since here is actually related to the span of time since the moment your parents met, rather than the first half of the sentence. Using that would be grammatically incorrect. However, you could say:
In this instance, that is used to create a relative clause, connecting the thirty years to the last half of the sentence. You can do this with other things too:
This isn't restricted to the present perfect, either:
But, as soon as you're talking about the span of time, you have to use since again.