1 Paris: I reiterate. We can't leave without paying. We can't break the law!
1 Serron 2: We can't not break the law!
2 Paris: This is no time to go into your personal psychological problems!
3 Spanners: He may be right. If we don't follow established history, then we could potentially cause a paradox and destroy the entire space-time continuum.
4 Paris: Hmmm. You might be changing my mind with that fact.
4 Serron 2: Oooh! You're certainly changing mine!

It's difficult to say what the consequences of causing a temporal paradox will be, without actually going ahead and doing it.

Of course we already know that history has been altered for the future Serron and Iki Piki, but that's not the same as causing an actual paradox.

Wait... or is it?

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2020-02-29 Rerun commentary: If we could cause a temporal paradox, you can bet your bottom dollar that someone would go ahead and do it.

So we may already have been shifted into variant timelines, many times over. It just so happens that we're now in the timeline where Abraham Lincoln wasn't really a vampire hunter, and the Titanic sank on its maiden voyage, and the Roman Empire lasted until 1973.