what does the sentence "I'd hate for anything to come between us" means?

"I'd hate for anything to come between us"

is grammatically correct and uses an idiom in its figurative sense:

come between (someone and someone else). TFD

• Lit. to be in between two people.
• Fig. to interfere in someone else's romance; to break up a pair of lovers.

The sentence means the same if you simply omit for:

• I'd hate anything to come between us.

The Oxford Modern English Grammar (p82) notes that this sentence structure with the omissible for is more common in American English:

Finally, we recognize for as a subordinating conjunction in clauses that do not carry tense, as in (171) . This construction is more frequent in American English.

• 171 There is nothing I want [_clause  for you to say anyway].