Does wake_up cause a race condition?

Question

I was looking at the wake_up function here from the linux kernel code

https://elixir.bootlin.com/linux/latest/source/kernel/sched/wait.c#L154

It's line 154

/**
 * __wake_up - wake up threads blocked on a waitqueue.
 * @wq_head: the waitqueue
 * @mode: which threads
 * @nr_exclusive: how many wake-one or wake-many threads to wake up
 * @key: is directly passed to the wakeup function
 *
 * If this function wakes up a task, it executes a full memory barrier before
 * accessing the task state.
 */
void __wake_up(struct wait_queue_head *wq_head, unsigned int mode,
            int nr_exclusive, void *key)
{
    __wake_up_common_lock(wq_head, mode, nr_exclusive, 0, key);
}

If it's waking up all the threads, couldn't this cause a race condition? Let's say all the threads are waiting for the same data structure or something, so once the wake_up is called, aren't all the threads racing for the same thing?