If our parents are still alive, should we say our "beloved parents"?
Sure.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
It's certainly easier to love some of your relatives more once they are dead; and it's also easier to say that, because the person isn't around to contradict or embarrass you. This might be why you have associated the term with relatives who have passed on.
Neverthless, "beloved" is appropriate to use in life, especially if it's true.