It would be great if you could change the date of my interview.
The sentence isn't correct grammatically. It should be:
It will be great if you can change the date of my interview
(conditional 1). or
It would be great if you could change the date of my interview
No doubt, in conditional 2 sentences, we talk about unreal or imaginary situations. But it's also a fact that when we want to be more polite for perfectly possible plans, suggestions, or requests in the present or future, we usually use the conditional 2 sentences, especially in business correspondence.
You can use either of the sentences, but to be more polite you should use the sentence #2. I think there is no difference in meaning. It's very common to say "I would appreciate if you could ........".