I'd argue that "event A happens before event B" is objectively true if and only if event A happens in event B's past light cone, and so there's no actual contradiction. The only weirdness you get is that if events A and B are space-like separated, none of the statements "event A happens before event B", "event A happens after event B", or "event A happens at the same time as event B" are objectively true. But you wouldn't say it's contradictory or paradoxical, just that it's a partial order rather than a total order.