The Many-Worlds Interpretation is a local (no FTL) and deterministic theory, though it works differently than what most people think of when they hear "deterministic theory of physics". Every possible outcome of a random quantum event occurs. (Technically the outcome space is continuous instead of discrete, but it's easier to talk about discrete outcomes.) If a human observes a random quantum event (which happens constantly), then there will be a separate version of the person for each outcome who observes that outcome.
However, even with a deterministic universe, there's still true randomness from the perspective of people in the universe. If you flip a quantum coin (that's appropriately set up to have a 50% chance either way and its output is dependent on some quantum random events), then it's impossible even in concept to predict which way it will land, because after the flip, there will be one version of you that sees it land heads and another version of you that sees it land tails.
However, even with a deterministic universe, there's still true randomness from the perspective of people in the universe. If you flip a quantum coin (that's appropriately set up to have a 50% chance either way and its output is dependent on some quantum random events), then it's impossible even in concept to predict which way it will land, because after the flip, there will be one version of you that sees it land heads and another version of you that sees it land tails.