I wouldn't consider the Hopper to have an abilifier. "Does not count for deck building requirements" is not an ability of any kind. It's "hop" ability is a special ability, which is negatable (if I am Salvation is active when it is drawn for instance). I don't know of any abilifiers that the hopper would have.
But I would definitely say that all identifiers are "active" at all times, since you can, say, search deck for a human EC with some cards, and human is an identifier.
