The more experiments you run in parallel, the more likely it becomes that at least one experiment's branches do not have an even distribution across all branches of all (combinations of) other experiments.
And the more experiments you run, whether in parallel or sequentially, the more likely you're to get at least one false positive, i.e. p-hacking. XKCD is using "find a subgroup that happens to be positive" to make it funnier, but it's simply "find an experiment that happens to be positive". To correct for p-hacking, you would have to lower your threshold for each experiment, requiring a larger sample size, negating the benefits you thought you were getting by running more experiments with the same samples.
And the more experiments you run, whether in parallel or sequentially, the more likely you're to get at least one false positive, i.e. p-hacking. XKCD is using "find a subgroup that happens to be positive" to make it funnier, but it's simply "find an experiment that happens to be positive". To correct for p-hacking, you would have to lower your threshold for each experiment, requiring a larger sample size, negating the benefits you thought you were getting by running more experiments with the same samples.